`lim_(x->0)x/(tanx)` is a. 1 b . 0 c. 4 d. not defined

Explanation

To solve the limit \( \lim_{x \to 0} \frac{x}{\tan x} \), we can use the Taylor series expansion for \( \tan x \) around \( x = 0 \).

### Step-by-Step Solution:

1. **Recall the Taylor Series Expansion for \( \tan x \)**:
The Taylor series expansion for \( \tan x \) around \( x = 0 \) is:
\[
\tan x = x + \frac{x^3}{3} + \frac{2x^5}{15} + O(x^7)
...