Question
Find the interval for which $f(x)=x^4-2 x^2$ is increasing or decreasing.
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→$\int\frac{1}{\sqrt{16-6\text{x}-\text{x}^2}}\text{ dx}$
Prove the following:
cos [tan–1 {sin (cot–1 x)}] = $\sqrt{\frac{\text{1 + x}^{2}}{\text{2 + x}^{2}}}$.
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Find the value of $\int_0^1 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x$.
→If $\vec{\text{a}},\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}+\vec{\text{b}}\big|=\big|\vec{\text{b}}\big|,$ then prove that $\vec{\text{a}}+2\vec{\text{b}}$ is perpendicular to $\vec{\text{a}}.$
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Let f : R → R be defined as $\text{f(x)}=\frac{2\text{x}-3}{4}.$ Write fof-1(1).
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Find the area of the parallelogram whose diagonals are:
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Show that $\text{f}\text{(x)}=\begin{cases}1+\text{x}^2,&\text{if } 0\leq\text{x}\leq 1\\2-\text{x},&\text{if }\text{x} > 1\end{cases}$ is discontinuous at x = 1.
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