Calculus Answers

Verify that y=e^2xsinx is a solution to the differential equation (d^2/dx^2)-(4dy/dx)+5y=0


(2) Differentiate ln(1+sin^2x)

(3) differentiate x^x
(4).Evaluate the integral [ (2x^3-4x-8)/(x^4-x^3+4x^2-4x)]dx

b) A wire of length 100 centimeters is cut into two pieces. One piece is bent to form a square. The other piece is bent to form an equilateral triangle. Find the dimensions of the two pieces of wire so that the sum of the areas of the square and the triangle is minimized.

Verify that y = e^2x sinx is a solution to the differential equation d^2 y/dx^2 − 4dy/dx + 5y = 0.

Find the volume of the solid generated by revolving the region bounded by the curves y = x^2 and y = 4x − x^2 about the line y = 6.

Use integration by parts to integrate x sec x tan x dx ∫
(2)
b) Integrate 3( x )1 4x 12x 5 dx 2
∫
+ + + (3)
c) Integrate dx
x( x()4 )1
x x 5

Find the length of the arc of the parabola y2 = x from (0, 0) to (1, 1)

find fx(0,0) and fx(x,y), where (x,y) not=(0,0) for the following functi on f(x,y)={xy^3/x^2+y^2, when (x,y)not =(0,0), 0 when (x,y)=(0,0)} is fx continuous at (0,0) justify

If ,
q= k 1/4 L 1/4
check the homogeneity

What is the volume of the solid obtained by rotating the region under the curve y=cosx between x=0 and x=π/12 about the x-axis.

An office supply company manufactures and sells X permanent markers per year at a price of P €/unit. The Price/Demand equation
for the markers is: