# Step-by-step Solution

## Find the limit of $x+\sin\left(x\right)$ as $x$ approaches $0$

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### Videos

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

## 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: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\left(\lim_{x\to0}\left(x\right)+\lim_{x\to0}\left(\sin\left(x\right)\right)\right)^{\tan\left(x\right)}$
2

Evaluating the limit when $x$ tends to $0$

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

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

Limits

~ 0.36 seconds