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Apply the formula: $\lim_{x\to c}\left(a^b\right)$$={\left(\lim_{x\to c}\left(a\right)\right)}^{\lim_{x\to c}\left(b\right)}$, where $a=1-4x$, $b=\frac{1}{x}$ and $c=0$
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${\left(\lim_{x\to0}\left(1-4x\right)\right)}^{\lim_{x\to0}\left(\frac{1}{x}\right)}$
Learn how to solve problems step by step online. (x)->(0)lim((1-4x)^(1/x)). Apply the formula: \lim_{x\to c}\left(a^b\right)={\left(\lim_{x\to c}\left(a\right)\right)}^{\lim_{x\to c}\left(b\right)}, where a=1-4x, b=\frac{1}{x} and c=0. Evaluate the limit \lim_{x\to0}\left(\frac{1}{x}\right) by replacing all occurrences of x by 0. Apply the formula: \frac{x}{0}=\infty sign\left(x\right), where x=1. 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:.
