# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{x-\sin\left(x\right)}{x-\tan x}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(x-\sin\left(x\right)\right)}{\frac{d}{dx}\left(x-\tan\left(x\right)\right)}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of (x-sin(x))/(x-tan(x)) as x approaches 0. If we try to evaluate the limit directly, it results in indeterminate form. Then we need to apply L'Hôpital's rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function.

$-\frac{1}{2}$$\,\,\left(\approx -0.5\right)$
$\lim_{x\to0}\left(\frac{x-\sin\left(x\right)}{x-\tan x}\right)$

Limits

10. See formulas

30

### Time to solve it:

~ 0.15 s (SnapXam)