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

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(B) We need to evaluate the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{(x+1)^{5}-1}{x}$Let $y = x+1$. As $x 	o 0$,$y 	o 1$.Substituting $y$ into

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$5$

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(B) We need to evaluate the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{(x+1)^{5}-1}{x}$Let $y = x+1$. As $x 	o 0$,$y 	o 1$.Substituting $y$ into the expression,we get:$\mathop {\lim }\limits_{y 	o 1} \frac{y^{5}-1}{y-1}$Using the standard limit formula $\mathop {\lim }\limits_{x 	o a} \frac{x^{n}-a^{n}}{x-a} = n a^{n-1}$:Here $n = 5$ and $a = 1$.$= 5 	imes (1)^{5-1}$$= 5 	imes 1 = 5$Therefore,$\mathop {\lim }\limits_{x 	o 0} \frac{(x+1)^{5}-1}{x} = 5$

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 0} \frac{(x+1)^{5}-1}{x}$

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