# Calculus Question

calculus multi-part question and need the explanation and answer to help me learn.

Requirements: JUST THE ASWER

10/13/23, 9:14 PMQuiz: Chain Rule Quizhttps://canvas.okstate.edu/courses/158491/quizzes/396437/take1/5Chain Rule QuizStarted: Oct 13 at 9:14pmQuiz InstructionsControls: The functions f(x) and g(y) are given in the picture above. You can clickbetween the checkboxes to show the output of the two different functions, f and g, onthe right screen. You can change the position of x or y along the left number line(depending on which function you are looking at) by dragging the blue dot or byentering a numerical value into the input box. On the left number line, the red andgreen tic-marks represent other values of x (or y) located fixed distances (multiples ofΔx or Δy) away from the blue dot. Changing “n” changes how many red (and green)tic-marks are viewable, which also changes the size of Δx (or Δy). On the rightnumber line, the red and green tic-marks show the corresponding output values of f(or g) at different x (or y) values. You can zoom in and out around x, y, f(x), or g(y) byclicking the corresponding “Zoom In” and “Zoom Out” buttons, which alter thenumber of tic-marks that are presented on screen.

10/13/23, 9:14 PMQuiz: Chain Rule Quizhttps://canvas.okstate.edu/courses/158491/quizzes/396437/take2/51 ptsQuestion 1Select the “Use f” checkbox. Set the input to and the size of to .25 (leftscreen, this happens when ). Which of the following correctly describe thecorresponding sizes of the intervals (right screen)? (Select all that are correct,Zoom in and out as needed to make your determination).They are all 4 times as large as and are oriented in the opposite direction as .They are all 2 times as large as and are oriented in the same direction as .They are all 4 times as large as and are oriented in the same direction as .They are all the same size.They get bigger as x gets bigger.They are all 2 times as large as and are oriented in the opposite direction as .They are all the same size as They get smaller as x gets bigger.1 ptsQuestion 2Select the “Use g” checkbox. Set the input to , set to be at most .5, andzoom out as much as possible in both windows. Which of the following correctlydescribe the corresponding sizes of the intervals (right screen)? They are all the same size.They get bigger as y gets bigger.They are all 2 times as large as .They get smaller as y gets bigger.They are all 3 times as large as .

10/13/23, 9:14 PMQuiz: Chain Rule Quizhttps://canvas.okstate.edu/courses/158491/quizzes/396437/take3/5They are all the same as .1 ptsQuestion 3Keep the function g active, and y at 1.5. As you decrease the size of (on the left),the sizes of the corresponding intervals on the right will also decrease. What elsedescribes what happens to the sizes of the corresponding intervals near the output on the right? (Zoom in and out as needed) (Note: You are seeing locallinearity)They become more evenly spaced.They become less evenly spaced.1 ptsQuestion 4Adjust until it has a size of .1, and zoom in near g(1.5) until the correspondingintervals on the right look indistinguishable from a linear function. Use the amounts ofchange, , to estimate . 1 ptsQuestion 5Suppose we wanted to find h'(1.5), where h(y)=f(g(y)). To estimate h'(1.5), we need tofirst estimate f'(x) for what value of x? (Select all that apply)x=f(1.5)x=g(1.5)

10/13/23, 9:14 PMQuiz: Chain Rule Quizhttps://canvas.okstate.edu/courses/158491/quizzes/396437/take4/5x=-3.25x=2.25x=1.51 ptsQuestion 6Estimate f'(x) for the value of x determined in Question 5. 1 ptsQuestion 7Use your results from Questions 4 and 6 to estimate h'(1.5)1.5 ptsQuestion 8Use similar reasoning to estimate , where .1.5 ptsQuestion 9

10/13/23, 9:14 PMQuiz: Chain Rule Quizhttps://canvas.okstate.edu/courses/158491/quizzes/396437/take5/5No new data to save. Last checked at 9:14pm Use similar reasoning to estimate , where .Submit Quiz