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a. Find the volume V(S) of the solid S by revolving the region R bounded by x 2 + y − 4 = 0 and x − y + 2 = 0 about y = 0. (6 pts.) b. Set-up the integral that represents V(S) when the region R in (a.) is revolved about x = −2. (4 pts.)
1. Find the dimension of a rectangle with perimeter 200 m and whose area is as large as possible
2. The sum of two positive numbers is 10. Find the numbers if the sum of their squares is a minimum
find the surface area of the object obtained by rotating y=4+3x^2, 1<=x<=2 about the y axis
Let f(x)= x^2/x^2-9
(a) Find the intervals where f is increasing and decreasing. Identify the relative
extrema.
(b) Find the intervals where f is concave up and down and identify any inflection points.
(c) Sketch a graph of f using the information from this problem
Decompose
(i)
(x^2+X+1)/(X+3)(x^2-x+1)
into partial fractions (show all the steps).
Using Greens theorm ..integration (3x+4y)dx+(2x-3y)dy for a circle
Graph the surface area of a cube as a function of the volume of a cube
∫4 sin 8t cos 3t dt
Integrate :
(1/2*sin2x-cos^2x)/(sin^2x-cos^2x)
𝑓(𝑥) = 2𝑥^3 + 𝑐𝑥^2 + 2𝑥
Suppose 𝑓 is differentiable on ℝ and has two roots. Show that 𝑓′ has at least one root.
