Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Solve using direct substitution
- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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As it's an indeterminate limit of type $\frac{\infty}{\infty}$, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is
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$\lim_{x\to0}\left(\frac{\frac{e^x-1}{x^3}}{\frac{x^3}{x^3}}\right)$
Learn how to solve problems step by step online. Find the limit of (e^x-1)/(x^3) as x approaches 0. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction \frac{x^3}{x^3} by x^3. The limit of a sum of two or more functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)).
