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Exercise

$\lim_{x\to\pi}\left(\frac{1-\sin\left(\frac{x}{2}\right)}{1+\cos\left(3x\right)}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to\pi }\left(\frac{1-\sin\left(\frac{x}{2}\right)}{1+\cos\left(3x\right)}\right)$ by replacing all occurrences of $x$ by $\pi $

$\frac{1-\sin\left(\frac{\pi }{2}\right)}{1+\cos\left(3\pi \right)}$
2

The sine of $\frac{\pi }{2}$ equals $1$

$\frac{1- 1}{1+\cos\left(3\pi \right)}$
3

Multiply $-1$ times $1$

$\frac{1-1}{1+\cos\left(3\pi \right)}$
4

Subtract the values $1$ and $-1$

$\frac{0}{1+\cos\left(3\pi \right)}$
5

Zero divided by anything is equal to zero

0

Final answer to the exercise

0

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  • Integrate by partial fractions
  • Product of Binomials with Common Term
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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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