Calculus Answers

Determine the surface area generated by revolving the arc 3y= 4x from x=0 to x=3 about the x-axis.

Find the area between the curves y^2 - y + x = 0 and y^2 = x + 3.

Find the centroid of the solid generated if the region bounded by y = 2- x^2, x=0, and y=0 is revolved about the y-axis.

Consider the R²−R function f defined by f(x,y) = x−2y. Prove from first principles that lim_{(x,y)→(2,1)} f(x,y)=0.

a company's profit function, in dollars, is given by P(x)=-0.3x^2+56.16x-638 where x is the number of items sold. in addition, the company has a marginal revenue function of MR(x)=-0.6x+76.16. determine the total cost for the company to produce 10 items.

the rate of change in sales of bicycles at ted's bicycle shop for the year 2001 is given by s(x)=x+7.5, where x represents the month number in 2001 (e.i. x=1 is January, x=2 is February, x=12 is December). is the shop sold 28 bicycles in the month of February, find the shop's total sales function, TS(x).

Show that the function f: R^2→R^2 given by

f(x,y) = (xy^3+1, x^2+y^2) is not invertible. Futher

check whether it is locally invertible at the point (2,1)

Find the surface area of the part of the sphere

x^2+y^2+z^2=9

lying above the ellipse

x^2/4 + y^2/9 =1

Let f: R^3→R be function defined by :

f(x,y,z)= |x+2y+z| . Show that f is not differentiable at the point (1,-1,1)

If z= x^3y+ 3xy^4 where x= sin 2t and y= cos^2t .

Find dz/dx |t=0 by using chain rule.