Bouvier :)

1. 4+9+14+…….+44

2. 1/(1*2)+1/(2*3)+1/(3*4)+……+1/(49*50)

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f(x)=cosx on [-pi/2,pi/2]; n=6

Since the function is symmetric over the y axis, then the left riemann sum and the right riemann sum equal each other right?

(Because for the left rs, there is an overestimation on quadrant 1, and underestimation on quadrant 2. And for the right rs, there is an overestimation on quadrant 2, and underestimation on quadrant 1.)

What would be the left and right riemann sums?

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f(x)=x+cosx on [0,2pi]

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Use the linear approximation to estimate the given function value (point a)

f(x)=x/(x+1)

a=1

f(1.1)

Compute the percent error

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Use the linear approximation to estimate the given function value (point a)

f(x)=sinx

a=pi/4

f(0.75)

Compute the percent error

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RIght circular cones of height h and radius r are attached to each end of a right circular cylinder of heigh h and radius r, forming a double pointed object. For a given surface area A, what are the dimensions r and h that maximize the volume of the object?

(Also, I have trouble imagining what the picture would look like)

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Find the max and min interval using the second derivative test:

h(t)=2+cos(t) for -pi =< t =< pi

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Find the intervals on which f is increasing and decreasing.

f(x) = cos^2(x) on [-pi,pi]

1. f(x) = x arcsinx, find f'(sqrt2/2)

2. g(x) = ln(arctanx), find g'(sqrt3)

The derivatives of both these equations will equal to zero right? Because u is a constant, so u'= 0, which means the whole thing will equal to zero.

Really?

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A spherical balloon is being inflated. Its volume increases at a rate of 2 cubic inches per second. How fast is the radius increasing when the radius in 3 inches?

The sides of a square increase at a rate of 1 inch/min. How fast is the area changing when the perimeter of the square is 12 inches?

f(x)=(x^3)-(2x^2)-5x+6 on [4,8]

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f(x)=x(sqrt(2-x^2)) on [-sqrt2, sqrt2]

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f(x)=(x)/(((x^2)+1)^2)

on [-2,2]

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The volume of a cube decreases at a rate of 0.5ft^3/min. What is the rate of change of the side length when the side lengths are 12 ft?

A rectangle initially has dimensions 2 cm by 4 cm. All sides begin increasing in length at a rate of 1 cm/second. At what rate is the area of the rectangle increasing after 20 seconds?

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