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Exercise

$\lim_{x\to0}\left(\frac{x^2+5x+4}{3x^3+6x-2}\right)^{\left(x^2+4x+3\right)}$

Step-by-step Solution

Learn how to solve limits of exponential functions problems step by step online. Find the limit of ((x^2+5x+4)/(3x^3+6x+-2))^(x^2+4x+3) as x approaches 0. Evaluate the limit \lim_{x\to0}\left(\left(\frac{x^2+5x+4}{3x^3+6x-2}\right)^{\left(x^2+4x+3\right)}\right) by replacing all occurrences of x by 0. Multiply 6 times 0. Subtract the values 0 and -2. Multiply 5 times 0.
Find the limit of ((x^2+5x+4)/(3x^3+6x+-2))^(x^2+4x+3) as x approaches 0

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Final answer to the exercise

$-8$

Try other ways to solve this exercise

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  • Integrate by partial fractions
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Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).

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