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3 questions
-2
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Explaining the zeroes of $x+\exp x$ [closed]
I want to know how can I explain why the function $x+ \exp x$ has a zero in $\mathbb{R}$? Where the equation $x+e^x=0$ can also be rewritten as $x=-e^x$
If anyone knows anything on how to begin such ...
user1128264
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2
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Prove an equation has exactly two real roots [closed]
If i want to prove and equation has exactly two real roots, how would i do so? What theorem would i use, Rolle's or Bolzano's or something else?
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2
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Calculate the integral $\int_{\varGamma}\frac{3e^{z}}{1-e^{z}}dz$
I am looking to solve
$$\int_{\varGamma}\frac{3e^{z}}{1-e^{z}}dz,$$ where $\varGamma$ is the contour $|z|=4\pi/3$.
We have been asked first to consider $e^{z}=1$ and $e^{z}=-1$ which I get to be $z=...
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