Class 12

Math

Calculus

Continuity and Differentiability

\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

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Find $dxdy $ of the functions given by $(cosx)_{y}=(cosy)_{x}$

Differentiate the functions with respect to x$cos(cx+d)sin(ax+b) $

Find $dxdy $ in the following: $y=cos_{−1}(1+x_{2}2x ),−1<x<1$

Show that the function defined by $g(x)=x[x]$ is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Find all points of discontinuity of f, where f is defined by$f(x)={x∣x∣ 0 ifx=0ifx=0 $

Find $dxdy $if $x−y=π$

Differentiate the functions with respect to x , $cos(sinx)$

Prove that every rational function is continuous.