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1) Differentiate the following functions (you don't have to simplify)
i. y=sqrt[(x-1)/(x4+1)]
ii. y=(sinx)lnx
2) A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?
3) After 3 days a sample of radon-222 decayed to 58% of its original amount.
A. What is the half-life of radon-222?
B. How long would it take the sample to decay to 10% of its original amount?
4) Use linear approximation to estimate the value of (2.001)5.
a) what will the unit price? b) what will be the profit at this rate of production
Find a maximum flow in the network below from the source S to the sink T. Justify that your flow is a maximum flow
Find the slope of the tangent line to f(x) = e2X2+3x at the point where x = 0. The function g is differentiable, and the tangent line to the graph of y = g(x) at x = -5 is y = 2x - 2. Let f(x) = -3g(x) + 5x + 5. Give f' (-5).
Find the general solution of the differential equation - Please show all work
An access ramp rises 3.2 ft over a distance of 30 ft. What is the average angle of the ramp with the horizontal?
Explain how you define the nodes xk that represent the dates above - Define a global interpolating polynomial Pr that passes through all data points given for the time of sunrise.
what is the equation for the inverse of y cosx 3? a. y arccos x 3 b. y arccos x - 3 c. y arccos x 3 d. y
Determine the volume of a sphere of radius r. A sphere is swept out when the region bounded by the x-axis and the top half of the circle x2 + y2 = r2 is revolved about the x-axis.
A semicircular plate rests on the x-axis, between x = -2 and x = 2. Assuming that the density of the plate varies with a continuous mass-density function given by ρ(y) = (1+y) gram / square cm, find the total mass of the plate.
Describe the euclidean algorithm applied to two consecutive Fibonacci numbers. Use your description to show that the euclidean algorithm can last arbitrarily many steps. So what can we say about how long does the euclidean algorithm last?
Fixed costs are estimated to be $8,400 for 2005. How many units should the company sell to break even ?
(a) How fast is the top of the ladder sliding down the wall? (b) At what rate is the area of the triangle formed by the ladder, wall, and the ground changing? (c) At what rate is the angle ! between the ladder and the ground changing?
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