Calculus Answers

Trace the curve y^2=(x+1)(x-1)^2 by showing all the properties you use to trace it?

A curve is such that dy/dx = 12/ (2x+1)squared . The point (1 , 1) lies on the curve .find the coordinates of the point at which the curve intersects the x axis

1. Evaluate D(sin(x²+3x-1))
2. Given that f(x)=3x-1
g(x)=cosx
h(x)=e^2x+1
Find (fogoh)x and (hogof)x
3. Evaluate lim[⅔x] x->6-, [•] in the greatest integer formula.
4. Find lim (x(x+1)(2+x))/x+x³
5. Find the different coefficient of (i) xlog5^x (ii) x³log8^x

1) Find dy/dx of the following using first principle
a) y = 1/√x
b) y = √x+1

2) Find the first derivative of the following :
a) y= e -1/2x +cosx sinx
b) y= √E ax sinx

3) Find dy/dx of the following :
a) sinx cosx/Cos2x
b) √x+1/ √x - 1

Find the directional derivatives of f(x,y,z)= x²+2y²+3z² at P₀(1,1,1) in the direction of a= i+j+k .

lim of squar root of x squared plus 3x plus 4 over x cubed plus 1

x approaches -1

Find the angle of intersection of r=a(1-cos(theta)) and r=2acos(theta)

a manufacture can sell x times. determine the total revenue function,profit function and level of output that will maximize profit

Find the directional derivatives of
f(x ,y ,z)= x²+2y²+3z² at P₀(1,1,1) in the direction of a = i+j+k.