Pertanyaan

Nilai x → 2 lim ( ( x 2 − 9 ) ⋅ tan ( 2 x − 4 ) x 2 + x − 6 ) = …

Nilai $x \to 2 lim (\frac{x ^{2} + x - 6}{( x ^{2} - 9 ) \cdot tan ( 2 x - 4 )}) = \dots$

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Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah .

nilai limit tersebut adalah negative 1 half

Pembahasan

Dengan demikian, nilai limit tersebut adalah .

$limit as x rightwards arrow 2 of open parentheses fraction numerator x squared plus x minus 6 over denominator left parenthesis straight x squared minus 9 right parenthesis times tan open parentheses 2 straight x minus 4 close parentheses end fraction close parentheses equals limit as x rightwards arrow 2 of open parentheses fraction numerator open parentheses x minus 2 close parentheses open parentheses x plus 3 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses x plus 3 close parentheses times tan space 2 open parentheses straight x minus 2 close parentheses end fraction close parentheses equals limit as x rightwards arrow 2 of open parentheses fraction numerator open parentheses x minus 2 close parentheses over denominator open parentheses x minus 3 close parentheses times tan space 2 open parentheses straight x minus 2 close parentheses end fraction close parentheses equals limit as x rightwards arrow 2 of open parentheses fraction numerator 1 over denominator left parenthesis x minus 3 right parenthesis end fraction times fraction numerator open parentheses x minus 2 close parentheses over denominator tan space 2 open parentheses straight x minus 2 close parentheses end fraction close parentheses equals limit as x rightwards arrow 2 of open parentheses fraction numerator 1 over denominator left parenthesis x minus 3 right parenthesis end fraction times 1 half close parentheses equals open parentheses fraction numerator 1 over denominator 2 minus 3 end fraction close parentheses open parentheses 1 half close parentheses equals negative 1 open parentheses 1 half close parentheses equals negative 1 half$

Dengan demikian, nilai limit tersebut adalah negative 1 half .