ข้อสอบ PAT 1 - กุมภาพันธ์ 2561

ข้อ 28

กำหนดให้ a open parentheses 0 close parentheses equals 1 และสำหรับ n equals 0 comma 1 comma 2 comma 3 comma space horizontal ellipsis ให้ begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style

พิจารณาข้อความต่อไปนี้

   ก. a open parentheses 3 close parentheses minus a open parentheses 1 close parentheses เป็นจำนวนเฉพาะ

   ข. a open parentheses 4 close parentheses greater than a open parentheses 5 close parentheses

   ค. a open parentheses 7 close parentheses equals 146 over 25

ข้อใดต่อไปนี้ถูกต้อง

รีวิว - เสียงตอบรับจากผู้เรียน
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด

เฉลยข้อสอบ

begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style
begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style

begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style

begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style

begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style
begin mathsize 12px style ด ั งน ั้ น thin space thin space thin space thin space thin space space limit as straight x rightwards arrow 4 of fraction numerator straight f apostrophe open parentheses straight x close parentheses minus straight f apostrophe open parentheses 4 close parentheses over denominator straight x minus 4 end fraction equals straight f apostrophe apostrophe open parentheses 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open square brackets straight f apostrophe open parentheses straight x close parentheses close square brackets subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals straight d over dx open parentheses 3 straight x squared minus 6 straight x close parentheses subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals right enclose 6 straight x minus 6 end enclose subscript straight x equals 4 end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 6 open parentheses 4 close parentheses minus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space equals 18 end style

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