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calc1-exam2s08

# calc1-exam2s08 - t is in seconds and s(t is in meters a...

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Math 111 EXAM 2o March 12,2ffi8 Read each problem carefirlly. Show all your work for each problem! Use only the methods discussed in class. No calculators! 1. (15 points) Differentiate the following functions: 2. (15 points) a) Findtheequationofthetangentlinetothecurve_ r3y - r2t' :4 atthepoint (2,L). b) Given the firnction r * cos(ry) : y, find # 3. (16 points) Use logarithmic differentiation to find # forthe following functions: w a) A - 4(W) - # *2tnr b) z : cscy(ev * coty) c) u - W a ) y : 5. b)U: @inr)" 4. (l5points) Differentiate the following functions: a) z:In(cscr) b)u: ffi c) ra: arcsin(c2) s(t) : 2f -9t2 +r2t+ 1, where (12 points) The positionof aparticle is given by
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Unformatted text preview: t is in seconds and s(t) is in meters. a) Find the velocity of the particle at time t. b) When is the particle at rest? When is it moving foward? When is it moving backward? c) Find the total distance traveled by the particle during the first 3 seconds. (15 points) Differentiate the following functions: a) U :[email protected]+t)5 b) " : *2([email protected] t7 c) y : coshfcot(Iogrr)] 7 - (12 points) A spherical balloon begins to leak air at t : 0 seconds. Its radius t seconds later is r(t) : ry inches. At what rate is air leaking from the balloon when f : 30 seconds 0"rr,o" : tn 13 )?...
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