# Tagged Questions

For basic questions about limits, derivatives, integrals, and applications, mainly of one-variable functions.

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### Differential problem, find the maximum and minimum value

Find the maximum, minimum value and inflection/saddle point of the following function $f(x)=12x^5-45x^4+40x^3+6$ $f(x)=x+\frac{1}{x}$ $f(x)=(2x+4) (x^2-1)$ Give a little explanation or procedural ...
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### How to graph gradient vector?

I'm working on a practice problem for my Calculus 3 course. It gives the function: $z=x^2+y^2$, and asks to graph the contours for $c=1,2,3$. Than asks to calculate the gradient at point $(2,1)$ and ...
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### Taylor series problem

Find and state the convergence properties of the Taylor series for the following: a.) $f(z)=z^3\sin 3z$ around $z_0=0$ b.) $f(z)= \frac{z}{(1-z)^2}$ around $z_0=0$ I know that the ...
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### find derivative of $e^{3\sqrt{x}}$ using chain rule.

im asked to find the derivative of this function using the chain rule. $$e^{3\sqrt{x}}$$ here are my steps. step 1 - identify the inner and outer functions. therefore I identified outer function ...
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### $\lim_{x\to \infty}A(x)$

If $A(x)=\int_{-1}^{x}e^{-|t|}dt$, then what is $\lim_{x\to \infty}A(x)$? I am not able to make any progress on this problem.I hope someone can help me with this.
I have an exercise where there is the following given: $f$ is a causal function. $f$ is Laplace transformable:$\int_{0}^{\infty} f(t)e^{-zt} \, dt = L(z)$ with $Real(z)> -1$ I have to ...