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Exercise

$\lim_{x\to0}\left(\frac{5x-1}{x^{5x}}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(\frac{5x-1}{x^{5x}}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{5\cdot 0-1}{0^{5\cdot 0}}$
2

Multiply $5$ times $0$

$\frac{5\cdot 0-1}{0^{0}}$
3

$0^0$ represents an indeterminate form

indeterminate

Final answer to the exercise

indeterminate

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
  • FOIL Method
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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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