MATH 231 WRITTEN ASSIGNMENT 2PLEASE ANSWER ALL QUESTIONS ON FORM PROVIDED USING DIGITAL EQUATION EDITOR IF POSSIBLE
Microsoft Word - written assignments_MAT-231-GS-mar21 Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top Module 4—Written Assignment 2 1. Points P(4, 2) and Q(x, y) are on the graph of the function f (x) = √?. Complete the following table with the appropriate values: y-coordinate of Q, the point Q(x, y), and the slope of the secant line passing through points P and Q. Round your answer to eight significant digits. 2. Use the value in the preceding exercise to find the equation of the tangent line at point P. 3. Consider the function f (x) = −x2 + 1 Sketch the graph of f over the interval [−1, 1]. 4. Approximate the area of the region between the x-axis and the graph of f over the interval [−1, 1] for problem 3. 5. Use the graph of the function y = f (x) shown here to find the values of the four limits, if possible. Estimate when necessary. Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 6. Use direct substitution to show that each limit leads to the indeterminate form 0/0. Then, evaluate the limit. 7. Use direct substitution to show that each limit leads to the indeterminate form 0/0. Then, evaluate the limit. For #8 and #9 - Use the following graphs and the limit laws to evaluate each limit. 8. 9. Copyright © 2021 by Thomas Edison State University. All rights reserved. Back to Top 10. In physics, the magnitude of an electric field generated by a point charge at a distance r in vacuum is governed by Coulomb’s law: Where E represents the magnitude of the electric field, q is the charge of the particle, r is the distance between the particle and where the strength of the field is measured, and 1/4πε0 is Coulomb’s constant: 8.988 × 109 N ꞏ m2 /C2. a. Use a graphing calculator to graph E(r) given that the charge of the particle is q = 10−10. b. Evaluate What is the physical meaning of this quantity? Is it physically relevant? Why are you evaluating from the right? For #11 and #12 - Determine the point(s), if any, at which each function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. 11. 12. 13. Decide if the function is continuous at the given point. If it is discontinuous, what type of discontinuity is it? For #14 and #15 - Find the value(s) of k that makes each function continuous over the given interval. 14. 15. 16. 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.