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Exercise

$\lim_{x\to0}\left(xsec\left(\frac{3\pi}{2}-x\right)\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(x\sec\left(\frac{3\pi }{2}-x\right)\right)$ by replacing all occurrences of $x$ by $0$

$0\sec\left(\frac{3\pi }{2}+0\right)$
2

$x+0=x$, where $x$ is any expression

$0\sec\left(\frac{3\pi }{2}\right)$
3

Any expression multiplied by $0$ is equal to $0$

0

Final answer to the exercise

0

Try other ways to solve this exercise

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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$\lim_{x\to-4}\left(\frac{x+4}{x^2-16}\right)$

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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