Final answer to the problem
indeterminate
Step-by-step Solution
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1
Evaluate the limit $\lim_{x\to\infty }\left(x\left(\arctan\left(e^x\right)-\frac{\pi }{2}\right)\right)$ by replacing all occurrences of $x$ by $\infty $
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$\infty \cdot \left(\arctan\left(e^{\infty }\right)-\frac{\pi }{2}\right)$
Learn how to solve problems step by step online. Find the limit of x(arctan(e^x)-pi/2) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(x\left(\arctan\left(e^x\right)-\frac{\pi }{2}\right)\right) by replacing all occurrences of x by \infty . Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value e. Evaluate the arctangent of +/- infinity. Combine fractions with common denominator 2.
Final answer to the problem
indeterminate
