Your last submission is used for your score. 1. –/3 points LarCalc11 3.5.012. Find lim h(x), if it exists. x →∞ f(x) = 9x2 + 2x + 7 (a) h(x) = lim h(x) = f(x) x x →∞ (b) h(x) = lim h(x) = f(x) x2 x →∞ (c) h(x) = lim h(x) = x →∞ f(x) x3 My Notes Ask Your Teacher 2. –/3 points LarCalc11 3.5.013. My Notes Ask Your Teacher My Notes Ask Your Teacher My Notes Ask Your Teacher Find each limit, if it exists. (a) (b) (c) 3. lim x →∞ lim x →∞ lim x →∞ –/1 points x7 + 9 x8 − 1 x7 + 9 x7 − 1 x7 + 9 x6 − 1 LarCalc11 3.5.017.MI. Find the limit, if it exists. lim x →∞ 4. 1+ –/1 points 8 x LarCalc11 3.5.019.MI. Find the limit, if it exists. lim x →∞ 5x + 7 7x − 4 5. LarCalc11 3.5.021. –/1 points My Notes Ask Your Teacher My Notes Ask Your Teacher My Notes Ask Your Teacher Find the limit, if it exists. 8x2 + x lim x → ∞ 8x3 + 6x2 + x 6. –/1 points LarCalc11 3.5.023. Find the limit, if it exists. lim x → −∞ 7. –/1 points 7x2 x +7 LarCalc11 3.5.033. Find the limit, if it exists. lim x →∞ 9 8x + sin x –/1 points 8. LarCalc11 3.5.034. My Notes Ask Your Teacher My Notes Ask Your Teacher My Notes Ask Your Teacher Find the limit, if it exists. lim 7 cos x →∞ –/2 points 9. 8 9x LarCalc11 3.7.005. Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum. (smaller value) (larger value) 10. –/2 points LarCalc11 3.7.007. Find two positive numbers satisfying the given requirements. The product is 432 and the sum of the first plus three times the second is a minimum. (first number) (second number) –/2 points 11. LarCalc11 3.7.009. My Notes Ask Your Teacher My Notes Ask Your Teacher My Notes Ask Your Teacher Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 200 and the product is a maximum. (first number) (second number) –/2 points 12. LarCalc11 3.7.011. Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 84 meters 13. length m width m –/2 points LarCalc11 3.7.013. Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. Area: 16 square feet ft (smaller value) ft (larger value) –/2 points 14. LarCalc11 3.7.019. My Notes Ask Your Teacher A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must contain 180,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What dimensions will require the least amount of fencing? x= m y= m 15. –/2 points LarCalc11 3.7.021. My Notes Ask Your Teacher A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if the total perimeter is 22 feet. x= ft y= ft 16. –/6 points LarCalc11 3.7.023.MI. My Notes Ask Your Teacher A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (1, 2) (see figure below). (a) Write the length L of the hypotenuse as a function of x. L= , x >1 (b) Use a graphing utility to approximate x graphically such that the length of the hypotenuse is a minimum. Find the value of x that produces the minimum value L. (Round your answer to three decimal places.) x= (c) Find the vertices of the triangle such that its area is a minimum. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = ( ) (x, y) = ( ) (x, y) = ( ) –/2 points 17. LarCalc11 3.7.025. A rectangle is bounded by the x-axis and the semicircle y = My Notes Ask Your Teacher 9 − x2 (see figure). What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value) –/2 points 18. LarCalc11 3.9.013. My Notes Use the information to find and compare Δy and dy. (Round your answers to three decimal places.) y = 0.9x9 Δy = dy = x =1 Δx = dx = 0.1 Ask Your Teacher –/2 points 19. LarCalc11 3.9.015. My Notes Ask Your Teacher Use the information to find and compare Δy and dy. (Round your answers to four decimal places.) y = x4 + 2 x = −5 Δx = dx = 0.01 Δy = dy = –/1 points 20. LarCalc11 3.9.019. My Notes Ask Your Teacher My Notes Ask Your Teacher Find the differential dy of the given function. (Use "dx" for dx.) y = 5x2 − 2 dy = –/1 points 21. LarCalc11 3.9.022. Find the differential dy of the given function. y = csc 6x dy = dx –/1 points 22. LarCalc11 3.9.025. My Notes Ask Your Teacher My Notes Ask Your Teacher Find the differential dy of the given function. y= 6 − x2 dy = –/2 points 23. LarCalc11 3.9.029. Use differentials and the graph of f to approximate the following. (Round your answers to two decimal places.) (a) f(3.9) ≈ (b) f(4.04) ≈ –/2 points 24. LarCalc11 3.9.037.MI. My Notes Ask Your Teacher The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in miles per hour. T = 2.5x + 0.5x2 Approximate the change and percent change in total stopping distance as speed changes from x = 45 to x = 46 miles per hour. (Round your answers to one decimal place.) dT = dT T = ft % 25. LarCalc11 3.9.039. –/2 points My Notes Ask Your Teacher The period of a pendulum is given by the equation shown below, where L is the length of the pendulum in feet, g is the acceleration due to gravity, and T is the time in seconds. T = 2π L g The pendulum has been subjected to an increase in temperature such that the length has increased by 2% (a) Find the approximate percent change in the period. % (b) Using the result in part (a), find the approximate error in this pendulum clock in 1 day. min Submit Assignment Home Save Assignment Progress My Assignments Copyright Request Extension 2020 Cengage Learning, Inc. All Rights Reserved
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