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Calculus and Analysis

Rate of change

1) The area of a circle is decreasing at the rate of 2 pie cm^2/s. At what rate is the radius of the circle decreasing when its area is 75 pie cm^2? 2)Find f'(-1), given f(y)=h(g(y)), h(2)=55, g(-1)=2, h'(2)=-1, and g'(-1)=7

Compound Interest Problems

If the tuition at a certain college is determined to cost $ 32000 in 10 years, how large must a trust fund that pays 7.5% compounded continuously be, in order for a child on her 8th birthday to ensure sufficient funds at age 18?

Differentiation/graphs

I have two problems (well, one problem with three parts and another one): 1. (a) Let f(x)=ax^2+bx+c, a does not equal zero, be a quadratic polynomial. How many points of inflection does the graph of f have? (b)Let f(x)=ax^3+bx^2+cx+d, a does not equal zero, be a cubic polynomial. How many points of inflection does the grap

Single-variable function

A robot is guided towards an object by a software algorithm that controls its position such that the path of the robot is approximately sinusoidal, with a period 2, as shown in Figure B4 (attached). (a) Show that the length l of any single-variable function f(x), between the limits of x=a and b, can be expressed by th

Mu''(t) + ku(t) = 0

Suppose m and k are positive numbers. Find u so that mu''(t) + ku(t)= 0 for all numbers t and u(0)=1 and u'(0)=2. (note: u'' = second derivative of u) Please clarify any shorthand that you are using. Thanks!

Ellipse, points where tangent line is vertical

Given the ellipse x2/4 + y2/9 = 1 What are the points where the tangent line is vertical? (In narrative, the problem reads: given the ellipse x squared divided by 4, plus y squared divided by 9, equals 1, what are the points where the tangent line is vertical? The problem is also attached in MS Word, in case you need it