Pertanyaan

Jika U ( x ) = 2 x 2 + 5 x − 7 dan V ( x ) = 3 x 2 + 8 x − 25 , maka nilai dari x → 3 lim x − 3 U ( x ) − V ( x ) adalah...

Jika $U (x) = 2 x^{2} + 5 x - 7$ dan $V (x) = 3 x^{2} + 8 x - 25$ , maka nilai dari $x \to 3 lim \frac{U ( x ) - V ( x )}{x - 3}$ adalah...

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Pembahasan

Jadi, jawaban yang tepat adalah C.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator U open parentheses x close parentheses minus V open parentheses x close parentheses over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator square root of 2 x squared plus 5 x minus 7 end root minus square root of 3 x squared plus 8 x minus 25 end root over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator square root of 2 x squared plus 5 x minus 7 end root minus square root of 3 x squared plus 8 x minus 25 end root over denominator x minus 3 end fraction cross times fraction numerator square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root over denominator square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses 2 x squared plus 5 x minus 7 close parentheses minus open parentheses 3 x squared plus 8 x minus 25 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative x squared minus 3 x plus 18 over denominator open parentheses x minus 3 close parentheses open parentheses square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative open parentheses x squared plus 3 x minus 18 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative open parentheses x minus 3 close parentheses open parentheses x plus 6 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative open parentheses x plus 6 close parentheses over denominator open parentheses square root of 2 x squared plus 5 x minus 7 end root plus square root of 3 x squared plus 8 x minus 25 end root close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 3 plus 6 close parentheses over denominator open parentheses square root of 2 times 3 squared plus 5 times 3 minus 7 end root plus square root of 3 times 3 squared plus 8 times 3 minus 25 end root close parentheses end fraction end cell row blank equals cell negative fraction numerator 9 over denominator square root of 26 plus square root of 26 end fraction end cell row blank equals cell negative fraction numerator 9 over denominator 2 square root of 26 end fraction end cell row blank equals cell negative 9 over 52 square root of 26 end cell end table end style$ Jadi, jawaban yang tepat adalah C.