calc1-finalexams08

calc1-finalexams08 - : 1 for the inital approximation and...

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Math 111 X'INAL EXAM May 9.2008 Read each problem carefully. Show all your work for each problem! No calculators! 1. (16 points) Find the derivatives of the following functions (do not simpliff): a) t:ffi b) g: rt("arctan(t3)1 c), : f""os(Lr)at d) u :ntn(seca) 2. (l6points) Giventhetunction y - V a) find the intervals on which the function is increasing or decreasing, b) find the intervals on which the function is concave up and concave down, c) find all asymptotes, and d) sketch a gaph of the function labeling local maxima, minima and inflection points (if they exist). 3. (8points) Giventheequationofthecurve sin@y) : cosr *1 a) find #, *d b) find the equation of the tangent line to the curve at the point (zr, 1) 4. (16 points) Evaluate the following integrals ^) I: # dt b) I ,,(2,"+D* a* c) I Y o" a) fot ,""ry (tan2y) ds 5. (8 points) Use Newton's Method a) to obtain an approximation for a solution of the equation 13 : I - 12. Use
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Unformatted text preview: : 1 for the inital approximation and find the nextapproximation r.2, drrd b) to obtain an approximation for { n . Use 11 : 3 for the initial approximation and find the second approximatiorr s2.@int let z : affi I 6. (8 points) A particle moves along a straight line and its acceleration is given by a - 4C - 2t + I. Its initial velocity is v(0) = 4 ftl min and its initial position is s(0) : 6 feet. Find the position function of the particle s(t). 7. (12 points) Evaluate the following limits: ") ]S ffi o, lS v@otns) ") l$(*-#-il d) lT. 1t+2,'1* 8. (Spoints) Findthepointontheparabola U:12 thatisclosesttothepoint (2,+). 9. (8 points) A tank that is in the shape of a cone stands with its vertex on the ground. The tank has water pumped into it at the rate of 6 ff/min. The cone is 9 feet highwith a base radius of 3 feet. How fast is the water level rising when the water is 4 feet deep? (Y"orn : #fh)...
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