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Step-by-step Solution

Find the limit of x+sin(x) as x approaches 0

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Answer

$0^{\tan\left(x\right)}$

Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(x+senx\right)^{tanx}$
1

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\left(\lim_{x\to0}\left(x\right)+\lim_{x\to0}\left(\sin\left(x\right)\right)\right)^{\tan\left(x\right)}$
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Evaluating the limit when $x$ tends to $0$

$\left(0+\lim_{x\to0}\left(\sin\left(x\right)\right)\right)^{\tan\left(x\right)}$

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Answer

$0^{\tan\left(x\right)}$
$\lim_{x\to0}\left(x+senx\right)^{tanx}$

Main topic:

Limits

Used formulas:

1. See formulas

Time to solve it:

~ 0.28 seconds