1. Find the derivatives, using the rules for differentiation.
b. r = sin(6²)cos(30)
d. u sint 3
a. Show that the point (v3,2) is on the curve z2 V3ry 2y2=5.
b. find the tangent line to the curve at this point
c. find the normal line to the curve at this point
(§3.7# 10) When a circular plate of metal is heated in an oven, its radius increases at the
rate of 0.01 cm/min. At what rate is the plate's aren increasing when the radius is 50 cm?
4. (§3.7#13) A 13 ft. ladder is leaning against a house when its base starts to slide away.
By the time the base is 12 ft. from the house, the base is moving at the rate of 5 ft/sec.
a. How fast the the top of the ladder sliding down the wall then?
b. At what rate is the area of he triangle formed by the ladder, wall. and ground changing
c. At what rate is the angle 0 between the ladder and the ground changing then?
5. Use the linear approximation f(TO + dx) 2 f(In) + f'(ro)dr to estimate
a. f(1.1), where f(x) : I3 x. (Take to = 1. da = 0.1.)
b. f(1.9), where f(x) Ith
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