Evaluate the given limit: mathop {lim }limits | vedclass

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Question

(A) At $x=2$,the expression takes the indeterminate form $\frac{0}{0}$.Factorizing the numerator: $3x^{2}-x-10 = 3x^{2}-6x+5x-10 = 3x(x-2)+5(x-2) = (x

Vedclass · Accepted Answer

$11/4$

Vedclass · Answer

(A) At $x=2$,the expression takes the indeterminate form $\frac{0}{0}$.Factorizing the numerator: $3x^{2}-x-10 = 3x^{2}-6x+5x-10 = 3x(x-2)+5(x-2) = (x-2)(3x+5)$.Factorizing the denominator: $x^{2}-4 = (x-2)(x+2)$.Thus,$\mathop {\lim }\limits_{x 	o 2} \frac{(x-2)(3x+5)}{(x-2)(x+2)} = \mathop {\lim }\limits_{x 	o 2} \frac{3x+5}{x+2}$.Substituting $x=2$: $\frac{3(2)+5}{2+2} = \frac{6+5}{4} = \frac{11}{4}$.

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 2} \frac{3x^{2}-x-10}{x^{2}-4}$

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