MATH 150 Midterm: MATH150 MATH150-MT2-c

105 views6 pages

turquoisegnu128

31 Jan 2019

School

Simon Fraser University

Department

Mathematics

Course

MATH 150

Professor

All

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

Document Summary

Midterm 2: [4 marks] mark each statement t (true) or f (false): T f if y = sin 3, then y = cos 3. T f d dx (cid:18) log x2 log x (cid:19) = 0 for all x > 1. T f if f (x) = g (x) for 0 < x < 1, then f (x) = g(x) for 0 < x < 1. T f an equation of the tangent line to the parabola y = x2 at ( 2, 4) is y 4 = 2x(x + 2). T f for all real values of x we have that d dx. T f for all functions f , if f (x) exists for all x, then f (x) exists for all x. T f if a particle has a constant acceleration, then its position function is a cubic polynomial. T f if f (c) exists, then lim x c f (x) = f (c).

Related Questions

5. (18 pts) Circle True if the statement is ALWAYS true; circle False otherwise. No explanations are required. Let f be a one-to-one function and f its inverse. (a) If the point (2, 5) lies on the graph off, then the point (5,2) lies on the graph of f. True False f (2) = 5 f-1 (5) = 2 (b) sin-1 (T) = 0 True False Since >1, ris not in the domain of sin-?; | or sin-1 (7) #0, since sin (0) = 0 # Iff and g are two functions defined on (-1, 1), and if (c) limg (x) = 0, then it must be true that lim[ f(x) g (x)] = 0. True False Let f (x) = 1 / x, if x #0, and f (0) = 4 and g(x) = x. Then lim g (x) = lim (x) = 0, but Lim ( f (x) g(x)] = lim [() x] = 18 0. Iffis continuous on (-1, 1), and if f (0) = 10 and lim g (x) = 2, (a) True False then lin (= 5. Because lim : (*) - Limx-of (*) .f(0) = 20 = 5 If f is continuous on [1, 3], and if f(1) = 0 and f(3) = 4, then the equation f(x) = (e) has a solution in (1, 3). True False Since f continuous on [1, 3), f(1) = 0 < < 4 = f (3), by the Intermidiate Value Theorem there exists a cin (1, 3) such that f (c) = . (f) Let f be a positive function with vertical asymptote x = 5. Then lim f (x) = +0. True False Let f (x) = 1, if x < 5, and f (x) ==, ifx>5. Then lim f (x) = +00, and therefore, X = 5 is a vertical asymptote. 5 - X So, f is a positive function with vertical asymptote x = 5 but lim f (x) + +co, since lim f (x) = + 0 + lim f (x) = 1, which means that lim f (x) does not exist.

Q1)

---------------------------------------------------------------------------------

Q2)

---------------------------------------------------------------------------------

Q3)

---------------------------------------------------------------------------------

Q4)

---------------------------------------------------------------------------------

Q5)

---------------------------------------------------------------------------------

Q6)

---------------------------------------------------------------------------------

Q7)

If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above

Number 4 please)

MATH 150 Midterm: MATH150 MATH150-MT2-c

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 150 Midterm: MATH150 MATH150-MT1-c

MATH 150 Final: MATH1501 MATH1501 FinalB

MATH 150 Study Guide - Midterm Guide: Algebraic Function, Inverse Function, Trigonometric Functions

Related Questions