Evaluate: mathop {lim }limits_{x to 1} frac{x | vedclass

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Question

(B) We use the standard limit formula: $\mathop {\lim }\limits_{x 	o a} \frac{x^n - a^n}{x - a} = n a^{n-1}$.Given expression: $\mathop {\lim }\limit

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(B) We use the standard limit formula: $\mathop {\lim }\limits_{x 	o a} \frac{x^n - a^n}{x - a} = n a^{n-1}$.Given expression: $\mathop {\lim }\limits_{x 	o 1} \frac{x^{15}-1}{x^{10}-1}$.Divide the numerator and denominator by $(x-1)$:$= \frac{\mathop {\lim }\limits_{x 	o 1} \frac{x^{15}-1}{x-1}}{\mathop {\lim }\limits_{x 	o 1} \frac{x^{10}-1}{x-1}}$.Applying the formula where $a=1$:$= \frac{15(1)^{14}}{10(1)^9} = \frac{15}{10} = \frac{3}{2}$.

Evaluate: $\mathop {\lim }\limits_{x \to 1} \frac{x^{15}-1}{x^{10}-1}$

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