Math 131 Take Home Quiz 5 Print Name_______________________________

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Pertaining to Differentials df=f '(t)dt

Section 3.9

1. The continuous compound interest formula for P dollars invested at 6% interest compounded continuously for t years is .

a) Find dA if dt is 6 months.

b) Find the approximate percent change in A if dt is 6 months.

2. The volume of a right circular cone is where r is the radius of the base and h is the vertical height. If h is fixed at 5 cm, then V is a function of r.

a) Find V(1) and find dV if r=1 and dr is 0.1.

b) Find the equation of the tangent line to V(r) at (1, V(1)). Approximate the value of V(1.1) using the tangent line.

Section 4.2 topic, Absolute Extrema

3. Find the absolute maximum and absolute minimum of on each interval.

a) [0, 4]

b) [-2, 1]

4.3 and 4.6

4. A cone is made from a sector of a circle of radius 2. See pictures above.

a) Find the radius of the base of the cone that will maximize the volume. Use the 2nd derivative test to show your answer maximizes V.

b) Given that the area of the sector of the circle is 2πr, find the radius that will maximize

V/A = V/(2πr). Show that r = h.

Sections 5.1 and 5.2

5. a) Find the left and right hand Riemann sums, , and their average for on [0, 2].

b) Find and their average for on [ -1, 2].

6. Use symmetry, geometry, and the properties of integrals to evaluate each integral, given that .