Calculus and Trigonometric Functions Quiz
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Calculus and Trigonometric Functions Quiz

Quiz: Derivative, Undefined Points, and Limit of Trigonometric Function Test your knowledge of calculus and trigonometric functions with this quiz. Find the derivative of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$, identify the points where the function is undefined, and calculate the limit of the function as $x$ approaches $\frac{\pi}{2}$.

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@DefeatedComprehension

Questions and Answers

What is the derivative of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$?

$f'(x)=\frac{2\sin^2x}{(1+\cos x)^2}$

At which points is the function $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ undefined?

$x=\frac{\pi}{2}+k\pi, : k\in \mathbb{Z}$

What is the limit of $f(x)=\frac{\sin x}{1+\cos x}\cdot \tan^3x$ as $x$ approaches $\frac{\pi}{2}$?

The limit is $\infty$

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