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Unformatted text preview: Worksheet for Section 2.3 Basic Diﬀerentiation Rules
V63.0121, Calculus I Spring 2010
1. Evaluate the derivative of each of the following functions. (i) y = 10 sin(x) + 6 (ii) h(x) = (2x − 3)(x + 2) (iii) y = 1 1 − x2 x (iv) y = √ 3 t2 − √ 4 t3 a (v) y = √ − x2 4 x3 (vi) y = a cos(v ) + c b +2 vv 1 (vii) x(t) = √ − x2 4 x3 1 2. An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the band is pulled downward and released, the mass oscillates vertically. The equation of motion is s = 2 cos t + 3 sin t, where s is measured in centimeters and t ≥ 0 is measured in seconds. We will take the positive direction to be downward. (a) Find the velocity and acceleration of the mass at time t. (b) Graph the velocity and acceleration functions. A graphing calculator may be helpful here. (c) When does the mass pass through the equilibrium position the ﬁrst time? (d) How far from its equilibrium position can the mass travel? (e) When is the speed of the mass the greatest? When is the mass speeding up? 2 ...
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