class 12

Math

Calculus

Continuity and Differentiability

Let $f:R→Randg:R→R$ be respectively given by $f(x)=∣x∣+1andg(x)=x_{2}+1$. Define $h:R→R$ by $h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$.The number of points at which $h(x)$ is not differentiable is

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Find all the points of discontinuity of f defined by $f(x)=∣x∣−∣x+1∣$.

\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}+{3}{x}^{{{2}}}-{33}{x}-{33}\text{for }\ {x}\gt{0} and g be its inverse such that kg'(2)=1, then the value of k is

Prove that the greatest integer function defined by $f(x)=[x],0<x<3$ is not differentiable at $x=1andx=2$.

Is the function defined by $f(x)=∣x∣$, a continuous function?

Find the derivative of / given by $f(x)=tan_{−1}x$assuming it exists.

If $x1+y +y1+x =0$, for, $−1<x<1,$prove that $dxdy =−(1+x)_{2}1 $.

Find the derivative of f given by $f(x)=sin_{−1}x$assuming it exists.

Prove that the function f given by $f(x)=∣x−1∣,x∈R$ is not differentiable at $x=1$