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Exercise

$\lim_{x\to0}\left(5sinx\right)^7tan\left(x\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(5\sin\left(x\right)\right)$ by replacing all occurrences of $x$ by $0$

$\left(5\sin\left(0\right)\right)^7\tan\left(x\right)$
2

The sine of $0$ equals $0$

$\left(5\cdot 0\right)^7\tan\left(x\right)$
3

Multiply $5$ times $0$

$0^7\tan\left(x\right)$
4

Calculate the power $0^7$

$0\tan\left(x\right)$
5

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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Main Topic: Limits

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

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