(D) The limit of a continuous function $f(x) = x^n$ as $x$ approaches $a$ is simply the value of the function at $x = a$. Since $f(x) = x^n$ is contin

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(D) The limit of a continuous function $f(x) = x^n$ as $x$ approaches $a$ is simply the value of the function at $x = a$. Since $f(x) = x^n$ is continuous for $x > 0$,we have: $\lim_{x \rightarrow a} x^n = a^n$

Class 11 Mathematics Limits and Derivatives Concept of limits, Evaluation of algebric limits

Easy

If $a > 0$ and $n \in R$,then $\lim_{x \rightarrow a} x^n = \dots$

AP EAMCET 2020 All AP EAMCET

A
$n a^n$
B
$(n-1) a^n$
C
$n a^{n-1}$
D
$a^n$

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Class 11

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Limits and Derivatives

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Concept of limits, Evaluation of algebric limits

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If $a > 0$ and $n \in R$,then $\lim_{x \rightarrow a} x^n = \dots$

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For each $x \in \mathbb{R}$,let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim_{x \to 0^+} \frac{x([x] + |x|) \sin [x]}{|x|}$ is equal to

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