# Tagged Questions

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### How to evaluate an integral of the form $\int \frac{dx}{-ax^2 + b}$?

I need to evaluate $\int \frac{dx}{-ax^2 + b}$ while both $a$ and $b$ are positive. I was blocked while I was trying $x=\tan\theta$ which turned $dx=\sec^2\theta\, d\theta$ This method didn't ...
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### A simple-looking rational limit

Please help me compute: $$\lim_{z\to 0}\frac{\sqrt{2(z-\log(1+z))}}{z}$$ I know the answer is 1 because I plugged it into Mathematica. Attempts with L'Hopital's Rule didn't work. This a step in an ...
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### Find all values $c$ such that $(x+1)/(x^2+2cx+4)$ has domain R

Word for word: Find all values of $c$ such that $f(x)=\frac{x+1}{x^2+2cx+4}$ has a domain R I really don't know where exactly to start. I'm not sure what it means by "a domain R"
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### There cannot exist a rational function $f: \mathbb{R} \to \mathbb{R}$ injective, not surjective

I was looking for a rational function $f: \mathbb{R} \to \mathbb{R}$ that looks like $\arctan$, in that it is injective not surjective well-defined on all $x\in \mathbb{R}$ (no vertical ...
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### How to evaluate $\int_0^1\frac{1+x^4}{1+x^6}\,dx$

$$\int_0^1\frac{1+x^4}{1+x^6}\,dx$$ Can anyone help me solve the question? I am struggling with this.
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### Negative exponents when multiplying polynomials

$$(4-t)(1+t^2)^{-1}$$ I am supposed to find the derivative of this but I am not sure if it means $$\frac{1}{(4-t)(1+t^2)^{-1}}\quad\text{or}\quad\frac{(4-t)}{(1+t^2)}$$ I have tried to look online for ...