MATH 1013 Study Guide - Midterm Guide: Intermediate Value Theorem

47 views3 pages

turquoisegnu128

16 Oct 2018

School

York University

Department

Mathematics and Statistics

Course

MATH 1013

Professor

All

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

Document Summary

Solution: [8 points] the graph of y = f(x) is given below. (a) explain, referring to the graph, why f has an inverse. The function is one-to-one. (b) what is f 1(1) Solution: since f( 1) = 1 it follows that f 1(1) = 1. (c) sketch the graph of y = f 1(x) on the provided axes. Solution: simplify each of the following expressions (a) [4 points] cos[sin 1( 1. 3)] : is the angle between . 2 that satis es sin = 1: this. So cos = (b) [4 points] cos 1(cos( . Solution: cos( is [0, ] and . 4 . (the key thing here is that the range of cos 1. 1: [8 points] sketch the graph of y = 3 cos(2x + . 2 ) on the provided axes: calculate the following limits (a) [3 points] x2 4. Solution: you must evaluate this one from the left and the right: x2 4.

Related Questions

Problem 1.

Consider the function f(x) = sin x cos x + 5 on the interval (0, 2Ï ).

a) Find the open interval(s) on which the function is increasing or decreasing.

b) Apply the First Derivative Test to identify all relative extrema.

Problem 2.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = (x - 2)³ (x - 1)

Problem 3.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = 2 sin x + cos 2x on [0, 2Ï ]

Problem 4.

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes.

g(x) = x â(9 - x²)

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed

Consider the function f(x) = sin x cos x + 5 on the interval (0, 2Ï ).

a) Find the open interval(s) on which the function is increasing or decreasing.

b) Apply the First Derivative Test to identify all relative extrema.

Problem 2.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = (x - 2)³ (x - 1)

Problem 3.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = 2 sin x + cos 2x on [0, 2Ï ]

Problem 4.

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes.

g(x) = x â(9 - x²)

MATH 1013 Study Guide - Midterm Guide: Intermediate Value Theorem

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 1013 Study Guide - Midterm Guide: Intermediate Value Theorem

MATH 1013 Study Guide - Midterm Guide: List Of Trigonometric Identities, Inverse Function

MATH 1013 Study Guide - Midterm Guide: Inverse Function

Related Questions