class 12

Math

Calculus

Continuity and Differentiability

Let $f:[−21 ,2]→R$ and $g:[−21 ,2]→R$ be functions defined by $f(x)=[x_{2}−3]$ and $g(x)=∣x∣f(x)+∣4x−7∣f(x)$, where [y] denotes the greatest integer less than or equal to y for $y∈R$. Then,

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Differentiate the following w.r.t. x:$g(gx),x>1$

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find $dxdy $.$x=2at_{2},y=at_{4}$

Find the second order derivatives of the functions given.$tan_{−1}x$.

Find the values of k so that the function f is continuous at the indicated point in$f(x)={kx+1cosx ifx≤πifx>π $ at $x=π$

Find $dxdy $, if $x_{32}+y_{32}=a_{32}$.

Verify Rolles theorem for the function $y=x_{2}+2,a=−2$and $b=2$.

Differentiate $(x_{2}−5x+8)(x_{3}+7x+9)$ in three ways mentioned below:(i) by using product rule(ii) by expanding the product to obtain a single polynomial.(iii) by logarithmic differentiation.Do they all give the same answer?

The function $f(x)=sin∣x∣$ is continuous for all x