Evaluate the Given limit: \(\lim_{x\rightarrow -1}\) \(\frac{x^{10}+x^5+1}{x-1}\)

Question

Let \( f(x) = \int \frac{(2 - x^2) \cdot e^x \cdot \sqrt{1 + x} \cdot (1 - x)^{3/2}}{dx} \). If \( f(0) = 0 \), then \( f\left(\frac{1}{2}\right) \) is equal to:

Answer 1

\(\lim_{x\rightarrow -1}\)\(\frac{x^{10}+x^5+1}{x-1}\)= \(\frac{(-1)^{10}+(-1)^5+1}{-1-1}\) = \(\frac{1-1+1}{-2}\) = \(-\frac{1}{2}\)

Evaluate the Given limit: \(\lim_{x\rightarrow -1}\) \(\frac{x^{10}+x^5+1}{x-1}\)

Solution and Explanation

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