# Tagged Questions

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

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### Defining derivatives and integrals for hyperoperations > 2

Derivatives and Integrals are continuous generalizations of the Forward Difference and Summation additive operators respectively. We can do the same with multiplication and get multiplicative calculus ...
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### Find an equation to the tangent line to the curve at the given point

\begin{align} x &= \cos t + \cos 2t, & y &= \sin t + \sin 2t, & \left(−1, 1\right) \end{align} Using the above information I found that $\;\frac{dy}{dx}\;$ is: \begin{align} \...
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### Kline calculus intuitive chapter 3 problem 14

I am starting to get frustrated as I am not able to comprehend these questions because they simply do not make sense to me. Here is the problem and answer to it. https://scienceanswers.wordpress.com/...
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### Slope of a Tangent without given x value

At what point on the graph of $y=-3x^3+2x-1$ is the tangent parallel to $y=2x+10$? Now do I solve this question algebraically or do I solve it graphically since there is no specific x value given to ...
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### I have to maximize this function involving absolute values

f(x) = $\frac{1}{1+|x|}$ + $\frac{1}{1+|x-2|}$ needs to be maximized. Maximizing this function means minimizing the denominators simultaneously. So I have to find the minimum value of 1+ $|x|$ and 1+...
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### How can this be minimized?

I have the following function of $x_1$ and $x_2$: $$e(x_1,x_2)= (x_1^2+x_2^2)(a+n)+2a(-x_1+x_1x_2-x_2)+a^2$$ where $a$ and $n$ are real numbers. I want to find the values of $x_1$ and $x_2$ that ...
### About the convergence of $\sum_{n=1}^\infty(-1)^n\tan(\frac{\pi}{n+2})\sin(\frac{n\pi}{3} )$ [on hold]
Does the series $$\sum_{n=1}^\infty(-1)^n\tan\left(\frac{\pi}{n+2}\right)\sin\left(\frac{n\pi}{3}\right )$$ converge and why? I think that Leibniz' test may be helpful, but I wasn't able to find a ...