Calculus Answers

if f is one - one onto and differentiablw on R, then (f^-1)'(6)=1/f'(6) .Is the statement tue or false.
Explain why

Let f (x) = {√-x ,if x <0
{3-x ,if 0《x <3
{(x-3)^2 ,if x>3
(A) Check whether for is discontinuous.if yes l,find where?
(B) Give a rough sketch of the graph of f.

How to solve a multivariable function using Lagrange multipliers

Can the intermediate value theorem be applied to show that there is a root of the equation x^5-x^3+3x-5=0 in the given interval ]1,2[?If yes , apply it

x^3-\frac{2}{x^2}+2
(1,3)

The function f(x,y,z) = e^(xyz) is integrable over [0,2] × [0,2] × [0,2] .

The function F : R^2 → R defined by F(x,y)= (y + 2 , x + y) is locally invertible at any (x, y)∈R^2.

Even if both the partial derivatives of f : R^2 → R
exist at a point (a,b) , the function f may still not be continuous at (a,b).

The complex function can be modelled by equation y=3x^2 x e^x3 Find the indefinite integral of function using substitution method

Solve the Taylor's expression
F(x,y)=e^xcosy. (π,0)