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1. 2. (b) RIGHT(2) (c) TRAP(2) (d) MID(2) 4 0 4 0 (b) Illustrate MID(2) graphically. Calculate the following approximations to (a) LEFT(2) 6x2 dx. 0 (a) Find MID(2) for Find TRAP(2) for (x2 + 1) dx. (x2 + 1) dx. Is this approximation an underestimate or an overestimate? underestimate overestimate Illustrate TRAP(2) graphically. Is this approximation an underestimate or an overestimate? underestimate overestimate 3. Use the table below to estimate MID(5) = 2 1 g(t) dt by MID(5). t 1.0 g(t) −2.2 t 1.6 g(t) −2.6 1.1 1.2 −1.6 −1.2 1.7 1.8 −2.7 −0.9 1.3 −0.8 1.9 0.3 1.4 1.5 −1.8 −2.1 2.0 2.1 1.1 1.4 4. Sketch the area given by the following approximations to underestimate. b a f(x) dx. Identify each approximation as an overestimate or an (a) LEFT(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (b) RIGHT(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (c) TRAP(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (d) MID(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate 5. Sketch the area given by the following approximations to underestimate. b a f(x) dx. Identify each approximation as an overestimate or an (a) LEFT(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (b) RIGHT(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (c) TRAP(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate (d) MID(2) Identify the approximation as an overestimate or an underestimate. overestimate underestimate 6. Sketch the area given by the following approximations to underestimate. b a f(x) dx. Identify each approximation as an overestimate or an (a) LEFT(2) Identify the approximation as an overestimate or an underestimate of the area. overestimate underestimate (b) RIGHT(2) Identify the approximation as an overestimate or an underestimate of the area. overestimate underestimate (c) TRAP(2) Identify the approximation as an overestimate or an underestimate of the area. overestimate underestimate (d) MID(2) Identify the approximation as an overestimate or an underestimate of the area. overestimate underestimate 7. Consider the following. Decide which approximation—left, right, trapezoid, or midpoint—is guaranteed to give an overestimate for more than one. Select all that apply.) left right trapezoid midpoint none of these 5 0 f(x) dx. (There may be Decide which approximation is guaranteed to give an underestimate. (There may be more than one. Select all that apply.) left right trapezoid midpoint none of these 8. Consider the following. Decide which approximation—left, right, trapezoid, or midpoint—is guaranteed to give an overestimate for more than one. Select all that apply.) left right trapezoid midpoint none of these 5 0 f(x) dx. (There may be Decide which approximation is guaranteed to give an underestimate. (There may be more than one. Select all that apply.) left right trapezoid midpoint none of these 9. Consider the following. Decide which approximation—left, right, trapezoid, or midpoint—is guaranteed to give an overestimate for more than one. Select all that apply.) left right trapezoid midpoint none of these 5 0 f(x) dx. (There may be Decide which approximation is guaranteed to give an underestimate. (There may be more than one. Select all that apply.) left right trapezoid midpoint none of these 10. The width, in feet, at various points along the fairway of a hole on a golf course is given in the figure. If one pound of fertilizer covers 190 square feet, estimate the amount of fertilizer needed to fertilize the fairway. (Round your answer to the nearest integer.) lb 11. Evaluate the improper integral ∞ e−0.4x dx. 0 Sketch the area it represents. 12. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ 1 dx 1 2x+3 13. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ 1 dx 1 (x+9)2 14. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ 2e− xdx 0 15. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ 8x dx 0 ex 16. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) 0 ex dx −∞ 6 + ex 17. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ −∞ z2+64 dz 18. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) 2 −1 du 0 u2−4 19.. Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. (If the quantity diverges, enter DIVERGES.) ∞ 8 dx x(ln x)2 20. The rate, r, at which people get sick during an epidemic of the flu can be approximated by r = 1200te−0.5t, where r is measured in people/day and t is measured in days since the start of the epidemic. (a) Sketch a graph of r as a function of t. (b) When are people getting sick fastest? t= (c) How many people get sick altogether? people

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