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# Analytic Geometry and Calculus I MAT 114

CSU Pomona

GPA 3.53

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This 9 page Class Notes was uploaded by Dr. Elody Harris on Saturday October 3, 2015. The Class Notes belongs to MAT 114 at California State Polytechnic University taught by Randall Swift Jr in Fall. Since its upload, it has received 33 views. For similar materials see /class/218202/mat-114-california-state-polytechnic-university in Mathematics (M) at California State Polytechnic University.

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Date Created: 10/03/15

Math 114 July 7 2011 Review Sheet If your Math 114 meets on Monday amp Wednesday your exam 1 is Wednesday July 13 If your Math 114 meets on Tuesday amp Thursday your exam 1 is Thursday July 14 The exam will cover chapter 2 sections 2 to 8 and chapter 3 sections 1 to 2 The following is a list of the topics which you may expect to appear on the exam Numerical and Graphical Limits Basic Limit Laws Continuity Evaluating Limits Algebraically 1 2 3 4 5 The lntermediate Value Theorem 6 The Derivative of a Function 7 Product and Quotient Rule 8 Rates of Change It is strongly recommended that you study the lecture notes and the assigned homework problems The following sample problems are meant as a guide but there may be a topic or technique we discussed that is not included here Please don7t assume that means it will not appear on the exam Here is a copy of an old exam Math 114 Exam 1 9 pts 1 Evaluate the following limits a lim33 14 Ans 5 b limlC w4 7 2mg 4s Ans 1 C lim 272 Z zaZ z 1 12 pts 2 Let fx be the function de ned as 2 3 for z lt 1 JCW 107 for1 2 6x 7 x2 for z gt 2 Show that f is continuous for z 31 17 2 Then compute the right and left hand limits at z 1 and 27 and determine whether f is left continuous7 right continuous or continu ous at these points Ans Sketch the graph You will see that f is right continuous at z 1 and continuous at m 2 12 pts 3 Determine the points at which the function is discontinuous and state the type of discontinuity removable7 jump7 in nite7 or none of these a 1 we 7 95 7 2 Ans In nite discontinuity at m 2 b l96 i ll 996 7 95 7 1 Ans Jump discontinuity at z 1 C M96 ll ll Ans Jump discontinuities at each integer value of x 12 pts 4 Evaluate the following limits a 3 7 lim z 72 7 Ans 12 b 1 1 4 1m 7 174 7 2 m 7 4 Ans l sinx 7 cos x lim 14 tanx 7 1 d 3x572x3z77 lim 1HW2547912 3 Ans 2 12 pts 5 Use the Intermediate Value Theorem to nd an interval of length containing a root of f 3 2 1 Ans 7 0 10 pts 6 Using the de nition of the derivative7 compute f a for f 3z24x2 at a 71 You must use the de nition to receive credit for this problem Ans f 71 72 10 pts 7 Sketch the graph of f for the function f shown in the gure 7 6 12 pts 8 Calculate the derivative of the function a fx 45 32 6 7f Ans f 204 6x 3x771 b gt 3t2 4t 7 7t3 2t 8 Ans g t 6t 4t3 2t 8 3t2 4t 7 73t2 2 c m 6 W Ans h 10 pts 9 Find all values of z where the tangent lines to y 2 7 5x 4 and y 72x 3 are parallel Ans z Math 114 August 2 2011 Review Sheet If your Math 114 meets on Monday amp Wednesday your exam 2 is Wednesday August 10 If your Math 114 meets on Tuesday amp Thursday your exam 1 is Thursday August 11 The exam will cover chapter 3 sections 3 to 10 and chapter 4 sections 1 to 2 The following is a list of the topics which you may expect to appear on the exam Derivatives of Trigonometric Functions Chain Rule lmplicit Differentiation Derivatives of Inverse Functions Derivatives of Exponential and Logarithmic Functions Related Rates Linear Approximations The Mean Value Theorem 599 7 SmP FS 3NF Extreme Values It is strongly recommended that you study the lecture notes and the assigned homework problems The following sample problems are meant as a guide but there may be a topic or technique we discussed that is not included here Please dont assume that means it will not appear on the exam It is advised that you practice differentiation and know the various formulas we have discussed Expect a lot of differentiation on this exam Here is a copy of an old exam Math 114 Exam 1 12 pts 1 Find the derivative of the following functions 3 f x3 sin z Ans f x3 cos x 3x2 sin z b i1tanz gltgti1itan Ans g z 12753532 C h tanse0 Ans h tan2 z S802 s sec z 10 pts 2 Find the derivative of the following functions a x 3 cos x 4 Ans f 4sinx 7 3x2z3 cos x 5 b gm 1nltlt1nxgt3gt Ans g z i zlnm 8 pts 3 Find the equation of the tangent line to we W9 at1 Ans y 3713912 ln7r s 71 W12 10 pts 4 Find the points on the graph of y2 x3 7 3x 1 where the tangent line is horizontal Ans 717 717 ixg 8 pts 5 Using logarithmic differentiation7 nd the derivative of zx21 m 1 7 zz21 1 2m 1 Ans39 y i m lt5 121 7 2m1gt 12 pts 6 A water tank in the shape of a right circular cone of radius 300 cm and height 500 cm leaks water from the vertex at a rate of 10 crnSrnin Find the rate at which the water is decreasing when it is 200 cm Recall that the volume of a right circular cone is V 32h 3 Ans The water level is decreasing at a rate of 221 gtlt 10 4 crnrnin 10 pts 7 Find the linearization of atx7r2 Ans L 732x 3 7r 7r 10 pts 8 Find the maximum and minimum values of y x5 7 s on the interval 02 Ans The minimum is f5 14 75349927 the maximum is f2 30 10 pts 9 Use Rolle7s Theorem to prove f 5 2x3 4 712 has at most one real root 10 pts 10 Find the critical points and the intervals on which the function y 3x4 8x3 7 6x2 7 24x is increasing or decreasing and apply the rst derivative test to each critical point Ans Critical points 0 727 7117 on 70072f on 7271 on 7171 and on 100f

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