Pertanyaan

x → 3 lim x − 3 2 − x + 1

$x \to 3 lim \frac{2 - x + 1}{x - 3}$

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Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction equals negative 1 fourth end style$

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$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction equals limit as x rightwards arrow 3 of fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction times fraction numerator 2 plus square root of x plus 1 end root over denominator 2 plus square root of x plus 1 end root end fraction equals limit as x rightwards arrow 3 of fraction numerator 4 minus open parentheses x plus 1 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction equals limit as x rightwards arrow 3 of fraction numerator 3 minus x over denominator left parenthesis x minus 3 right parenthesis open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction equals limit as x rightwards arrow 3 of fraction numerator negative 1 times up diagonal strike open parentheses x minus 3 close parentheses end strike over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction equals limit as x rightwards arrow 3 of fraction numerator negative 1 over denominator 2 plus square root of x plus 1 end root end fraction equals fraction numerator negative 1 over denominator 2 plus square root of 3 plus 1 end root end fraction equals fraction numerator negative 1 over denominator 2 plus square root of 4 end fraction equals fraction numerator negative 1 over denominator 2 plus 2 end fraction equals negative 1 fourth end style$

Jadi, $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction equals negative 1 fourth end style$