alexandercollege.ca/courses/3525/assignments/75909 nter Onupter Due Sunday by 23:59 Points 54 Submitting an external tool Available 4 Apr at 0:00 - 9 Apr at 23:59 6 days ements Chapter 4 Test (a.k.a. "Midterm 3") 1hr28mins X Progr Score: 0/54 0/9 answered ins Question 1 G8 pts 9 1 = 19 0 Details ents A rotating light is located 10 feet from a wall. The light completes one rotation every 5 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall. wall light a feet per second Answer is a positive value. Give your answer accurate to at least one decimal place. Submit Question Question 2 5 pts 9 1 7 19 0 Details The function f(x) = 2x3 - 39x2 + 240x + 9 has one local minimum and one local maximum. 520 LTeet per second Answer is a positive value. Give your answer accurate to at least one decimal place. Submit Question Question 2 5 pts 9 1 2 19 0 Details The function f(x) = 2x - 39x + 240x + 9 has one local minimum and one local maximum. This function has a local minimum at a equals with value and a local maximum at a equals with value Submit Question Question 3 15 pts 9 1 = 19 0 Details Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 10 inches by b - 8 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume.m 3 X + exandercollege.ca/courses/3525/assignments/75909 Question 3 15 pts 9 1 = 19 0 Details Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 10 inches by b - 8 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume. 15 6 8 9 10 1 Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume V as a function of x: V = (2) Determine the domain of the function V of x (in interval form): (3) Expand the function V for easier differentiation: V = (4) Find the derivative of the function V: V'_Im 3 X + lexandercollege.ca/courses/3525/assignments/75909 (3) Expand the function V for easier differentiation: V (4) Find the derivative of the function V: V'- (5) Find the critical point(s) in the domain of V: (6) The value of V at the left endpoint is (7) The value of V at the right endpoint is (8) The maximum volume is V (9) Answer the original question. The value of a that maximizes the volume is:erm 3 X + alexandercollege.ca/courses/3525/assignments/75909 Question 4 2 pts 91 = 19 0 Details The function graphed above is decreasing on the interval The inflection point is at x = Submit Question Question 5 5 pts 9 1 = 19 0 Details Consider the function f(x) - 6(x - 4)"/. For this function there are two important intervals: (-0O, A) and (A, oo) where A is a critical number. Find AWWW? ' Consider the function f(:) = 6(z 4)\"3 _, and (A, 00) where A is a critical number. . For this function there are two important intew ls For each of the following interVals, tell whether f(.'E) is concave up (type in CU) or concave idown' 2:320, A): _! , (Amy; _} Midterm 3 X + as.alexandercollege.ca/courses/3525/assignments/75909 Question 6 G 7 pts 9 1 2 19 0 Details B 16 Q A cone-shaped cup is made from a circular piece of paper of radius 16 by cutting out a sector and joining the edges AC and BC. Find the maximum capacity (volume ) of such a cup Submit Question Question 7 2 pts 1 1 2 19 0 Details Use L'Hospital's rule to determine the following limit. Use exact values. 1 - cos 10x lim120 La. "Midterm 3' X + canvas.alexandercollege.ca/courses/3525/assignments/75909 Question 7 2 pts 9 1 = 19 0 Details Use L'Hospital's rule to determine the following limit. Use exact values. 1 - cos 10x lim 1-0 1- cos 7x Submit Question Question 8 6 pts 9 1 2 19 0 Details Use Newton's method to approximate a root of the equation e.97- - 6 - x as follows. Let x1 = 1 be the initial approximation. The second approximation x2 is and the third approximation x3is Submit Question . Question 9 4 pts 1 = 19 0 DetailsX + candercollege.ca/courses/3525/assignments/75909 Use Newton's method to approximate a root of the equation e"- = 6 - x as follows. Let x1 = 1 be the initial approximation. The second approximation x2 is and the third approximation x3is Submit Question Question 9 4 pts 9 1 2 19 0 Details Consider the function f() = - on the interval [4, 12). Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4, 12) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Submit