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Questions and Answers
What is the derivative of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$?
What is the derivative of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$?
- $f'(x)=\frac{\sin x}{1+\cos x}\cdot (3\tan^2x-\tan x)$
- $f'(x)=\frac{\sin x}{1+\cos x}\cdot \tan^2x$
- $f'(x)=\frac{2\sin^2x}{(1+\cos x)^2}$ (correct)
- $f'(x)=\frac{\sin x}{1+\cos x}\cdot (3\tan^2x+\tan x)$
At which points is the function $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ undefined?
At which points is the function $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ undefined?
- $x=\pi+k\pi, \: k\in \mathbb{Z}$
- $x=2\pi+k\pi, \: k\in \mathbb{Z}$
- $x=\frac{3\pi}{2}+k\pi, \: k\in \mathbb{Z}$
- $x=\frac{\pi}{2}+k\pi, \: k\in \mathbb{Z}$ (correct)
What is the limit of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ as $x$ approaches $\frac{\pi}{2}$?
What is the limit of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ as $x$ approaches $\frac{\pi}{2}$?
- The limit does not exist
- The limit is $\infty$ (correct)
- The limit is $0$
- The limit is $1$
