Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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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Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$
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${\left(\lim_{x\to0}\left(1-3x\right)\right)}^{\lim_{x\to0}\left(\frac{1}{x}\right)}$
Learn how to solve problems step by step online. Find the limit of (1-3x)^(1/x) as x approaches 0. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. Evaluate the limit \lim_{x\to0}\left(\frac{1}{x}\right) by replacing all occurrences of x by 0. An expression divided by zero tends to infinity. As by directly replacing the value to which the limit tends, we obtain an indeterminate form, we must try replacing a value close but not equal to 0. In this case, since we are approaching 0 from the left, let's try replacing a slightly smaller value, such as -0.00001 in the function within the limit:.
