Question

Thevalue of lim is

x→0

e^x-sinx-1/x​

Answer 1

Answer:

The answer is 0

Step-by-step explanation:

  $\displaystyle \lim_{x\to 0}\frac{e^x-\sin x-1}{x}$

$=\displaystyle \lim_{x\to 0}\frac{(e^x-1)-\sin x}{x}\\=\displaystyle \lim_{x\to 0}\frac{e^x-1}{x}-\displaystyle \lim_{x\to 0}\frac{\sin x}{x}\\=1-1=0$

( Using the formulas $\displaystyle \lim_{x\to 0} \frac{\sin x}{x}=1$ and $\displaystyle \lim_{x\to 0}\frac{e^x-1}{x}=1$