# Tagged Questions

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

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### $\int f(x)\,dx - \int f(x)\,dx$

which is true $$\int f(x)\,dx - \int f(x)\,dx = 0$$ or $$\int f(x)\,dx - \int f(x)\,dx=c\text{ ?}$$ with $c$ some arbitary constant. My intuition says that 'something' subtracted by itself is ...
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### What relationship between t and k would make the lines with Cartesian equations sx-ky+7=0 and tx+2y-3=0 perpendicular?

What relationship between t and k would make the lines with Cartesian equations sx-ky+7=0 and tx+2y-3=0 perpendicular?
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### What is the derivative of $x^i$?

What would the derivative be of $x^i$? Would it simply be $ix^{(1-i)}$? I tried running the Power rule, and I got that is that right?
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### Deriving a minimal amount of different size squares to fill a space from a function

Suppose we have many of squares of the following sizes: $1\times 1, 2\times 9, 3\times 5$ and we want to fill a board of size $16\times 32$ with squares such that we use a minimal amount of squares ...
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### Determine a set of parametric equations for the xz plane.

How do you determine a set of parametric equations for the $xz$ plane?
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### False proposition then true

Please, take a look to this inequation (m is a natural number): $$2\sqrt {m+1} - 2\sqrt m \lt\ \frac{1}{\sqrt{m+1}}$$ For m = 3, the expression is false: 0.53 $\lt$ 0.5 So, the expression doesn't ...
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### Proving that the roots of $1/(x + a_1) + 1/(x+a_2) + … + 1/(x+a_n) = 1/x$ are all real

Prove that the roots of the equation: $$\frac1{x + a_1} + \frac1{x+a_2} + \cdots + \frac1{x+a_n} = \frac1x$$ are all real, where $a_1, a_2, \ldots, a_n$ are all negative real numbers.
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### Evaluate $\int \frac{\sqrt{64x^2-256}}{x}\,dx$

$$\int \frac{\sqrt{64x^2-256}}{x}\,dx$$ Image. I've tried this problem multiple times and cant seem to find where I made a mistake. If someone could please help explain where I went wrong I would ...
### If $A$ and $B$ are positive constants, show that $\frac{A}{x-1} + \frac{B}{x-2}$ has a solution on $(1,2)$ [on hold]
If $A$ and $B$ are positive constants, show that $$\frac{A}{x-1} + \frac{B}{x-2}$$ has a solution on $(1,2)$. Please, support your answers with rigorous proof.
Limit Comparison Test Problem The three series $\sum A_n$, $\sum B_n$, and $\sum C_n$ have terms $$A_n=\frac1{n^9}, B_n=\frac1{n^4}, C_n=\frac1n.$$ Use the Limit Comparison Test to compare the ...