Microsoft Word - written assignments_MAT-231-GS-mar21 (1) Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 17. For #18 - #20 - Find δ in terms of ε using the formal...

MODULE 6 MATH 231 WRITTEN ASSIGNMENT 3 QUESTIONS ( 1-20) ONLY.PLEASE ANSWER ALL QUESTIONS ON FORM PROVIDED USING DIGITAL EQUATION EDITOR IF POSSIBLE or re write clearly and neatly as possible in order.


Microsoft Word - written assignments_MAT-231-GS-mar21 (1) Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 17. For #18 - #20 - Find δ in terms of ε using the formal limit definition. 18. 19. 20. Module 6—Written Assignment 3 1. For the following position function y = s(t) = t2 − 2t, an object is moving along a straight line, where t is in seconds and s is in meters. Find: a. the simplified expression for the average velocity from t = 2 to t = 2 + h; b. the average velocity between t = 2 and t = 2 + h, where (i) h = 0.1, (ii) h = 0.01, (iii) h = 0.001, and (iv) h = 0.0001; and c. Use the answer from a. to estimate the instantaneous velocity at t = 2 second. 2. For the function f (x) = x3 − 2x2 − 11x + 12, do the following. a. Use a graphing calculator to graph f in an appropriate viewing window. Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top b. Use the ZOOM feature on the calculator (or web graphing) to approximate the two values of x = a for which mtan = f ′(a) = 0. 3. For the following exercises, use the definition of a derivative to find f ′(x). f(x) = 4x2 4. For the following exercises, use the graph of y = f (x) to sketch the graph of its derivative f ′(x). 5. Suppose temperature T in degrees Fahrenheit at a height x in feet above the ground is given by y = T(x). a. Give a physical interpretation, with units, of T′(x). b. If we know that T′ (1000) = −0.1, explain the physical meaning. 6. Find the equation of the tangent line T(x) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. 7. assume that f (x) and g(x) are both differentiable functions for all x. Find the derivative of the function h(x). 8. Assume that and are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivative. Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 9. Find a quadratic polynomial such that f (1) = 5, f ′ (1) = 3 and f ″(1) = −6. 10. The given function represents the position of a particle traveling along a horizontal line. a. Find the velocity and acceleration functions. b. Determine the time intervals when the object is slowing down or speeding up. 11. A ball is thrown downward with a speed of 8 ft/s from the top of a 64-foot-tall building. After t seconds, its height above the ground is given by s(t) = −16t2 − 8t + 64. a. Determine how long it takes for the ball to hit the ground. b. Determine the velocity of the ball when it hits the ground. 12. Find the derivative dy/dx for 13. Find the equation of the tangent line to the given function at the indicated values of x. Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct. 14. Find the second derivative for y = sin x cos x 15. The amount of rainfall per month in Phoenix, Arizona, can be approximated by y(t) = 0.5 + 0.3cost, where t is months since January. Find y′ and use a calculator to determine the intervals where the amount of rain falling is decreasing. 16. Find the derivative for the function: 17. Find the equation of the tangent line to the graph of the given equation at the indicated point. Use a calculator or computer software to graph the function and the tangent line. Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 18. If the surface area of the rectangular box is 78 square feet, find dy/dx when x = 3 feet and y = 5 feet. 19. Find the derivative for 20. Find the equation of the tangent line to the graph of x3 − xlny + y3 = 2x + 5 at the point where x = 2. (Hint: Use implicit differentiation to find dy/dx.) Graph both the curve and the tangent line.) Module 8—Written Assignment 4 1. 2. You and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. You both leave from the same point, with you riding at 16 mph east and your friend riding 12 mph north. After you traveled 4 mi, at what rate is the distance between you changing? 3. Consider a right cone that is leaking water. The dimensions of the conical tank are a height of 16 ft and a radius of 5 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks water at a rate of 10 ft3/min? 4. A tank is shaped like an upside-down square pyramid, with base of 4 m by 4 m and a height of 12 m (see the following figure). How fast does the height increase when the water is 2 m deep if water is being pumped in at a rate of 2/3 m3/sec?