Calculus Answers

Given: x^2[f(x)]^2=9; and f9-10=3 Find f''(-1) by implicit differentiation.

Given: x^2[f(x)]^2=9; and f(-1) Find f''(-1) by implicit differentiation.

the gamma function of( -1) and of (0)?

Given that z=e^xy, x=2u+v, y=u/v .Use a chain rule to find

a) ∂z/∂u
b) ∂z/∂v

Given x^2-y^2+2uv+15=0 and x+2xy-u^2+v^2-10=0

Show that ∂u/∂x=u(1+2y)-2xv / 2(u^2+v^2) and ∂u/∂y=xu+vy / u^2+v^2

Evaluate
2 2x
a) ∫ ∫ (4x+2)dydx
0 x^2

1 y √1-y^2
b) ∫ ∫ ∫ z dzdxdy
0 0 0

1 √1-x^2
c) ∫ ∫ (x^2+y^2)^3/2 dydx
-1 0

Given the triple integral

∭(x^2+y^2)^3/2 dxdydz ,
A

A={(x,y,z):4≤x^2+y^2≤9, 1≤z≤2 }

Sketch the solid A and evaluate the integral

Sketch the region of integration for the integral
2 2x
∫ ∫ (4x+2)dydx
0 x^2
and write an equivalent integral with the order of integration reversed. Hence, evaluate the integral.

Find all the local maxima, local minima and saddle points of the function f(x,y)=x^3+y^3+3x^2-2y^2-8

Use the method of Lagrange multipliers to find the maximum and minimum values of the function f(x,y) = 3x + 4y on the circle x^2 + y^2 = 1