Math 124 C Spring 2023 Midterm II
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Math 124 C Spring 2023 Midterm II
May 16, 2023
1. (16 points) Compute dx(dy) for the following.
(a) 
(b) tan(x + y) − 4x3y2 = exy
(c) y = (1 + x2)5x
2. (11 points) A curve is given parametrically by
x = 2t2 − 40 y = t3 − 12t.
You can use the graph to see if your answers make sense, but your answers must be supported by your calculus and algebra work for credit.
(a) Find the equation of the tangent line to the curve at the point ( −38, − 11).
(b) The tangent line intersects the curve again at another point. Find the coordinates of that point.
3. (13 points) Use linear approximation near x = 1 to estimate a root b of the polynomial
p(x) = 4x3 − x2 + 3x − 7.
Is the approximate value of b you found more than or less than the actual value of b? Explain. A number b is a root of a polynomial p(x) if p(b) = 0 .
4. (10 points) There is a lighthouse on a small rocky island 2 kilometers from the dock. It has a rotating light. On a clear and sleepless night you observe that the light from the lighthouse sweeps your house at a rate of 4 meters per second moving towards the dock. If your beach house is 3 kilometers from the docks, how fast is the light of the lighthouse turning? Give your answer in radians per second and in revolutions per minute. Be careful with the units. The picture is not to scale.
2023-11-18