# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{\left(1-e^x\right)}{\tan\left(x\right)}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(1-e^x\right)}{\frac{d}{dx}\left(\tan\left(x\right)\right)}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of (1-e^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 the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1. The derivative of a sum of two functions is the sum of the derivatives of each function.

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### Problem Analysis

$\lim_{x\to0}\left(\frac{\left(1-e^x\right)}{\tan\left(x\right)}\right)$

Limits

~ 0.07 seconds