1. [-/3 Points] DETAILS LARCALC11 3.5.012. Find lim h(x), if it exists. X - 00 f( x ) = 3x1 (b) Use a graphing utility to approximate x graphically such that the length of the hypotenuse is a minimum. 6 8 10 -2 -8 -B O -10- O -10 10 10 2 O 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) = CL (x, ) ) = ( (x, y ) = (1T. [-12 Points] DETAILS LARCALC11 3.7.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A rectangle is bounded by the xaxis and the semicircle y = '2' 25 _ x2 {see figure]. What length and width should the rectangle have so that its area is a maximum? |:| (smaller value) {larger 1value} Need Help? W W 1B. [-12 Points] DETAILS LARCALC11 3.9.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the informalion to nd and compare r and dy. {Round your answers to three decimai places.) y=.5x\" x=1 Ax=dx=.1 19. [42 Points] DETAILS LARCALE11 3.9.015. [ MY NOTES ] [ ASK YOUR TEACHER ] [ PRACTICE ANOTHER Use the information to nd and compare Av and fly. (Round 1,rour answers to four decimal places.) y=x4+4 x=1 Ax=dx=.01 M" = l:| me: Need Help? 2. [-/3 Points] DETAILS LARCALC11 3.5.013. Find each limit, if it exists. X + 7 (a) lim X-0 y10- 3 + 7 (b) lim X -00 x .9 - 3 X + 7 (c) lim x -+ 00 10 - 320. [-/1 Points] DETAILS LARCALC11 3.9.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the differential dy of the given function. (Use "dx" for dx.) y = 7x- - 5 dy Need Help? Read It Watch It 21. [-/1 Points] DETAILS LARCALC11 3.9.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the differential dy of the given function. y = CSC 8X dy )dx Need Help? Read It 22. [-/1 Points] DETAILS LARCALC11 3.9.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the differential dy of the given function. y = V9 - x2 dy Need Help? Read It- mem W Use differentials and the graph of fto approximate the following. {Round your answers to two decimal places.) 24. [-1'2 Points] DETAILS LARCALC1 1 3.9.0315\". MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The total stopping distance Tof a vehicle is shown below, where Tis 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 = 20 to x = 21 miles per hour. {Round your answers to one decimal place.) 25. [-32 Points] DETAILS LARCALC11 3.9.939. MY NOTES ASK YOU R TEACHER PRACTICE ANOTHER The period of a pendulum is given by the equation shown below, where .L is the length of me pendulum in feet. g is the acceleration due to gravity, and Tis the me in seconds. T=21Ir i Q We pendulum has been subjected to an increase in temperature such ihat the length has increased by 1% (3) Find the approximate percent change in the period. :92. (b) Using the result in part (a), nd the approximate error in this pendulum clock in 1 day. S min Need Help? 3. [-/1 Points] DETAILS LARCALC11 3.5.017.MI. Find the limit, if it exists. lim 3 + IN X -0 X Need Help? Read It Master ItFind the limit, if it exists. 4x + 9 lim X -0 5x - 2Find the limit, if it exists. 3x- + X lim X - 00 2x# + 9x- + x Need Help? Read It Watch It 6. [-/1 Points] DETAILS LARCALC11 3.5.023. Find the limit, if it exists. lim x - -w x+ 9 Need Help? Read It 7. [-/1 Points] DETAILS LARCALC11 3.5.033. Find the limit, if it exists. 3 lim x - co 3x + sin xlim 9 cos 1 X - 00 4x Need Help? Read It /2 Points] DETAILS 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) Need Help? Read It Watch It [-/2 Points] DETAILS LARCALC11 3.7.007. Find two positive numbers satisfying the given requirements. The product is 768 and the sum of the first plus three times the second is a minimum. (first number) (second number) Need Help? Read It Watch It [-/2 Points] DETAILS LARCALC11 3.7.009. Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 320 and the product is a maximum. (first number) (second number) Need Help? Read It Watch It
