APPM 1350 Midterm: appm1350fall2017exam1_sol

34 views4 pages

turquoisegnu128

31 Jan 2019

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Fall 2017: (19 pts) using the function f (x) plotted in the gure, nd the following values, or write dne if they (cid:58) do not exist. Solution: (a) lim x 2 f (x) = dne (d) f (1) = dne (b) lim x 2 f (x) = 2 (e) lim x 2 f (x) = 3 (c) lim f (x) = 0 (f) f ( 3 x 2+ 5 ) = 4 (g) the average rate of change of f on(cid:2) 2, 1. 2(cid:3) is (h) the values of x in ( 3, 3) where f is not differen- 2 tiable are 2, 0, 1, 2 : (10 pts) use the graph of f (x) shown above to sketch a graph of the derivative f (x). Solution: here are two possible solutions. (cid:58: (17 pts) the following problems are not related. powered by (a) if tan = 1/x, < < 3 .

Related Questions

1. (18 pts) The graph of a function f, defined on (-0, +o), is given in the figure below. - - y = f(x) - - - - - - N - - 4 A -2-1 144 -1 - - - - - - - -- - - -- Use the graph of f to answer questions (a)-(f) below. (a) Determine the value or write "does not exist". i. f(-3) = -2 ii. f(0) = 1 (b) Determine the limit or write "does not exist" (DNE). Write "does not exist" only if a limit does not exist and is not too or -0. i. lim f(x) = 0 iv. lim f(x) = +00 X- 3 x2 ii. lim f(x) = -4 v. lim f(x) = -0 X- 0- x -00 iii. lim f(x) = DNE vi. lim f(x) = -2 x0 x++00 (C) MULTIPLE CHOICE! Circle ONLY one answer! Find a number a for which the following statement is true (the function f is shown above): STATEMENT: The function f is continuous at a, and lim f(x) = 0. i. a=-3 iii. a=0 V. a=3 ii. a = -2 iv. a = 2 vi. Such a number does not exist. (d) Determine the largest intervals of continuity of f. Use interval notation to write your answer. (-0, -3), (-3,0), (0, 2), (2, +00) (e) Write the equation(s) of all vertical asymptotes of f. Write "none" if appropriate. x= 2 (f) Write the equation(s) of all horizontal asymptotes of f. Write "none" if appropriate. y = -2

4. (21 pts) Let g be the function given by ( 6 - X 2 + x if x < 2, x + -2 g(x) = x2 – x-1 if x>2. (a) (6 pts) Use the definition of continuity to determine whether the function g is continuous at 2. Show your work. (b) (3 pts) Evaluate the limit. Justify your answer. Show your work. Write "does not exist" only if the limit does not exist and is not + or -0. lim g(x) = lim -2+ = +00 X 2 + X since the form of the limit is NUM: POS, DENOM: POS (c) (2 pts) Write the equation(s) of all vertical asymptotes of g. Write "none" if appropriate. The result in part (b) implies that the line x= -2 is a vertical asymptote. This is the only vertical asymptote, since the function g is continuous on its domain (d) (2 pts) Determine the largest) intervals of continuity of g. Use interval notation to write your answer. Let g be the function given by 12+ if x < 2, x# -2 2 + x g(x)= x2-x-1 x-1 if x>2. (e) (6 pts) Evaluate each limit. Do not use L'Hôpital's Rule. Write "does not exist" only if the limit does not exist and is not too or -00. Show your work. 6-1 i lim g(x) = lim -00 2 + X = lim -002 + x 0-1 + 1 x -00 x x x -+- 2 +1 0 0 + 11 x2 - x-1 1 ii. lim g(x) = lim x++ V x2 – x-1 X-1 x2 - x-1 X - 1 = lim x +oc x +0 - lim Vam M93001 (f) (2 pts) Write the equation(s) of all horizontal asymptotes of g. Write "none" if appropriate.

3. (18 pts) Show your work. Let f be a function defined by f(x) = x12 (a) Write the form of the limit and evaluate the limit. Do not use L'Hôpital's Rule. Show your work. 12 12 - 40=(0) - -= lim - 2 = * + 2) = Lima (68–1672 - FORM: (b) Find the natural) domain off. Write your answer in interval notation. (-0, -2) (-2, +00) (c) Let f-1 be an inverse of f. Find an expression for f-1(x), for x in the domain of f-1. = y(x + 2) = 12 yx + 2y = 12 = xy = 12 - 2y = 12 - 2y x= -- x= 12 - 2, and by switching x and y, we get y= 12 - 2 f(x) = 12 (d) Find the value or say "does not exist" (DNE). 1.84(f(n)) = 1 ii. f(p-10)) = DNE, because 0 is not in the domain of f-1

APPM 1350 Midterm: appm1350fall2017exam1_sol

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

APPM 1350 Midterm: appm1350summer2016exam1_0

APPM 1350 Midterm: appm1350spring2014exam1_sol

APPM 1350 Midterm: appm1350spring2013exam1

Related Questions