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Unformatted text preview: 5. (8 points) Find the equation of the tangent line to the graph of y = 4arctansc at the point
where ac = 1. Then use it (or the differential) to approximate the value of 4arctan(l.02). d
6. (10 points) Find i at the point (0, O) for the curve accos('y) + ycos(:n) = O. 7. (10 points) Find the point (56,19) on the line y = 2x -l- 1 if the distance from the point
(3, 2) to the point (33,31) is as small as possible. 8. (10 points) The graph of a function f is shown below. (a) Sketch the graph of f’.
(b) Sketch the graph of f”. 9. (10 points) The graph of a function y = f(:z:) is shown below. Use a Riemann sum with 4
subintervals to find 8 upper estimate for] f(:c) dx.
—1 13. (10 points) A ball is thrown downward from the top of a 600—foot building with an initial speed of 40
feet per sec0nd. It accelerates downward clue to gravity at 32 feet per second per second.
(In this problem it is important to express your answers in proper units.)
(a) Find a formula for the height of the ball at time t seconds after the start.
(b) When does the ball hit the ground? - ( 14 10 points) The function f is defined as follows
—:132 a: g —1
f($)= 1+2$ —-1<5L‘Sl (a) Sketch the graph of f.
(b) Find all values of cc at which f is NOT continuous.
(c) Find all values of m at which f is NOT differentiable. 15. (20 points) Sketch the graph of the function f on the interval (—oo,oo). based on the
following information. Show intervals of increase and decrease, and concavity. Label all
local maxima and minima and points of inflection (cc-coordinates) and any asymptotes. (i) f(0) = 1
(ii) to) = $2 _ 4
—8:B (iii) fllxl I m
(iv) 1'1111 ﬁx) 2 1. III—+00 (v) 11m f(a:) = 1. m—r—oo 4 ...
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- Spring '11
- Calculus, Mathematical analysis, Continuous function