Find the limit of $x^2\left(e^{\frac{1}{x^2}}-1\right)$ as $x$ approaches 0

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of x^2(e^(1/(x^2))-1) as x approaches 0. Multiply the single term x^2 by each term of the polynomial \left(e^{\frac{1}{x^2}}-1\right). Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2.