By Jon Rogawski
The scholar recommendations handbook to accompany Rogawski's unmarried Variable Calculus deals worked-out options to all odd-numbered workouts within the textual content.
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5 3 7. 08)t dollars. 99, 1], (a) What are1],the units of1]. theUse ROC (t)? 9999, thisoftofestimate the instantaneous velocity at t = 1. 5] and [0, 1]. 5. SOLUTION (a) The units of the rate of change of f (t) are dollars/year or $/yr. 08)t over the time interval [t1 , t2 ] is given by f f (t2 ) − f (t1 ) . 5 is approximately $8/yr. In Exercises 9–12, estimate the instantaneous rate of change at3 the point indicated. The distance traveled by a particle at time t is s(t) = t + t. Compute the average velocity over the time interval 2 − 3; xthe 4] = and4xestimate velocity at t = 1.
Exercises In Exercises 1–22, evaluate the limits using the Limit Laws and the following two facts, where c and k are constants: lim x = c, x→c 1. lim x x→9 SOLUTION lim x = 9. x→9 lim x x→−3 lim k = k x→c 46 CHAPTER 2 LIMITS 3. lim 14 x→9 SOLUTION 5. lim 14 = 14. x→9 lim (3x + 4) lim 14 x→−3 x→−3 SOLUTION We apply the Laws for Sums, Products, and Constants: lim (3x + 4) = lim 3x + lim 4 x→−3 x→−3 x→−3 = 3 lim x + lim 4 = 3(−3) + 4 = −5. x→−3 7. x→−3 lim (y + 14) lim 14y y→−3 y→−3 SOLUTION lim (y + 14) = lim y + lim 14 = −3 + 14 = 11.
Then f (g(t)) = f (12t + 9) = (12t + 9)4 as desired. the following three angles and find the values of the six 39. What is thethe period of the function g(θ ) = Sketch points on the unit circle corresponding 2 standard trigonometric functions at each angle: SOLUTION of 4π . Because 4π is a 2π The function sin 2θ has a period 7ofπ π , and the function sin(θ /2) has a 7period π (a) of π , the period of the function g(θ(b) (c) multiple ) = sin 2 θ + sin θ /2 is 4 π . 3 4 6 Assume that sin θ = 4 π , where < θ < π .