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If x = t^3 + y^3 where t= a cos v , y= Vsin v. Find dx/dv
If the sum of the surface areas of a sphere and a cube is fixed, what is the ratio of
the radius of the sphere to the edge of the cube when the sum of their volumes is
least
Use differentials to approximate the volume of material needed to make a rubber ball if the
radius of the hollow inner core is 2 𝑖𝑛., and the thickness of the rubber is 1
8
𝑖𝑛.
A differentiable function f has the property that f(5)=3
f′(5)=4 Whats the estimate for f(4.8) using the local linear approximation for f at x= 5 ?
Area Between Curves, Volumes and Average Values of Functions:
1 Calculate the area between the parabola 𝑦=𝑥2 and the line 𝑦=4
2 Derive the formula for the volume of the right-circular cone using a single integral given that 𝑦=−𝑎ℎ(𝑧−ℎ).
3. Find the average value 𝑓(𝑥)̅̅̅̅̅̅ of 𝑓(𝑥)=2𝑥2+3𝑥+3 in the interval [1,4].
What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?
given 1/u+1/v=1/f with f as a constant. if f=10 cm and u decrease with the rate of 2 cm/second, find the rate of v when u=40 cm
Find the derivative λ0(x) of the following function with respect to x:
λ(x) = f(x) · g(x) + f(x) · h(x) − g(x) · h(x)
using Leibniz theorem find the third derivative of the function y =2x
If three sides of a trapezoid are each 6 inches long, how long must the fourth side be if the area is a maximum?
