Find the limit of $\left(1-6x\right)^{\frac{1}{x}}$ as $x$ approaches 0

Learn how to solve limits of exponential functions problems step by step online. Find the limit of (1-6x)^(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:.