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Exercise

$\lim_{x\to1}\:\ln\left(x^9-1\right)$

Step-by-step Solution

1

The limit of a logarithm is equal to the logarithm of the limit

$\ln\left(\lim_{x\to1}\left(x^9-1\right)\right)$
2

Evaluate the limit $\lim_{x\to1}\left(x^9-1\right)$ by replacing all occurrences of $x$ by $1$

$\ln\left(1^9-1\right)$
3

Calculate the power $1^9$

$\ln\left(1-1\right)$
4

Subtract the values $1$ and $-1$

$\ln\left(0\right)$
5

$\ln(0)$ grows unbounded towards minus infinity

$- \infty $

Final answer to the exercise

$- \infty $

Try other ways to solve this exercise

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  • 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
  • FOIL Method
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