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# Math 110 Calculus 1Please answer all the questions below. alt="截屏2020-01-04上午2.21.29.png" />  Attachment 1 Attachment 2 Attachment 3 ATTACHMENT PREVIEW Download attachment 截屏2020-01-04上午2.21.29.png 2. The table gives the position of a particle moving along the x-axis as a function of time in seconds, where x is in meters. What is the average velocity of the particle ﬁomt=0tot=4? 27(t) answer : -1 4. Figure 2.6 shows a particle's distance from a point. What is the particle’s average velocity fromt = 0 to t = 3‘? disim (mate's) 3(a) 5 3 1 H590} 2 4 Figure 2.6 “Swer : 1 6. At time t in seconds. a particle‘s distance 3(t). in mi— crometers (pm). from a point is given by s(t) = e‘ — 1. What is the average velocity of the particle from t = 2 to t = 4? answer : (e4-ez)/(4-2) 8. In a time of t seconds, a particle moves a distance of .9 meters from its starting point, where s = 3t? (a) Find the average velocity between t = 1 and t = 1+am (i) h = 01, (ii) h = 0.01, (iii) h = 0.001. (11) Use your answers to part (a) to estimate the instan- taneous velocity of the particle at time t = 1. ATTACHMENT PREVIEW Download attachment 截屏2020-01-04上午2.21.41.png 22. Find the average velocity over the interval 0 S t S 0.2, and estimate the velocin at t = 0.2 of a car whose posi- tion. .9. is given by the following table. t(scc) 0 0.2 0.4 0.6 0.8 1.0 5(ft) 0 0.5 1.3 3.8 6.5 9.6 Use algebra to evaluate the limits in Problems 25— 26. 2 3 25_ um W 26, um (1_+’l)__1. h—m h h—HD h Homework (3) l. The table shows values of ﬁre) = :03 near a = 2 (to three decimal places). Use it to estimate f ’ (2). a: 1.998 1.999 2.000 2.001 2.002 x3 1.976 7.988 8.000 8.012 8.0%: 3. The income that acompany receives from selling an item is called the revenue. Production decisions are based. in part, on how revenue changes if the quantity sold changes; that is, on the rate of change of revenue with respect to quantity sold. Suppose a company‘s revenue. in dollars. is given by R{q) = 100:; — 10:12, where q is the quantity sold in kilograms. (a) Calculate the average rate of change of R With re- spect to q over the intervals 1 S q S 2 and 2gq5&amp; (b) By choosing small values for h, estimate the instan- taneous rate of change of revenue with respect to change in quantity at q = 2 kilograms. 1]. Figure 2.19 shows the graph of 1&quot;. Match the derivatives in the table with the points a, b, c, d, e. Figure 2.19 ATTACHMENT PREVIEW Download attachment 截屏2020-01-04上午2.21.48.png Figure 2.19 Use algebra to evaluate the limits in Problems 35-40. 35. lim (-3+ h)2 -9 h-0 h 37. lim 1/(1 + h) - 1 h-+0 h Find the derivatives in Problems 41-46 algebraically. 41. f(x) = 5x2 at x = 10 43. g(t) = t2 + tatt = -1 Homework 4 In Exercises 19-20, find a formula for the derivative using the power rule. Confirm it using difference quotients. 19. k(x) = 1/x 20. 1(x) = 1/22 Find a formula for the derivatives of the functions in Exer- cises 21-22 using difference quotients. 21. g(x) = 2x2 - 3 22. m(x) = 1/(x + 1)

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