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Calculus I

by: Braeden Lind

Calculus I MA 141

Braeden Lind
GPA 3.93


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This 5 page Study Guide was uploaded by Braeden Lind on Thursday October 15, 2015. The Study Guide belongs to MA 141 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 140 views. For similar materials see /class/223729/ma-141-north-carolina-state-university in Mathematics (M) at North Carolina State University.

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Date Created: 10/15/15
Calculus Study Guide for Test 1 Revised December 2002 The first test is primarily precalculus review You should be able to 1A Know the characteristics of and be able to distinguish between linear power log and exponential functions independent of whether the functions are given in tabular form by formulas or graphically Know the effect of changing the m and b in mx b the a and n in ax the P0 and a in Poa Be able to work straightforward applications that make use of any of these functions 1B Graph the basic functions sinx c0sx and tanx lC Graph simple polynomial and rational functions lD Know understand and be able to explain the concepts of domains ranges increasing and decreasing when applied to any function lE Know what the vertical line test is Know what the horizontal line test is Understand and be able to explain the concept of one to one functions and inverse functions how to find inverse functions in simple cases Know how to graph functions and their inverses on the same graph for any onetoone function lF Given an f x be able to construct the new functions f cx f x c f x c 1 f x Be able to explain the relationship of these new functions to the old in simple terms lG Remember that the tests are taken individually so go back and start with a clean sheet of paper and rework all of the homework problems together with above problems by yourself without looking at your notes or the textbook lH Conic Sections Recognize circles parabolas ellipses and hyperbolas in an equation and be able to graph them Calculus Study Guide for Test 2 Revised December 2002 You should be able to 2A i ii 2B 2C 2D Parametric Curves Plot simple parametric curves by assigning values of t Plot parametric curves by eliminating the parameter Limits Explain what it means for a function to have a limit at a point Explain left and right limits Apply the limit theorems and the Squeeze Theorem De ne vertical and horizontal asymptotes in terms of limits Continuity Verify that a function is continuous at a point and on an interval using the definition of continuity Locate the discontinuities of functions and explain why they are in fact discontinuities Explain what it means for a function to be differentiable at a point and on an interval Know how to apply the Intermediate Value Theorem to approximate roots of equations The Derivative Be able to explain the concept of a derivative in geometric terms For example on a graph of fx you should be able to indicate the following fa fah fahfaa in fah fa 1 fah fa h 256 h 39 Explain the derivative concept in practical terms such as distance speed and velocity the cooling or warming of an object Determine the units of the derivative given the units of the independent variable and the function iii Find the derivative at a point of simple functions algebraically iv Sketch the graph of the derivative of a function given a graph of the function v Sketch a possible graph of a function given the graph of its derivative Calculus Study Guide for Test 3 Revised December 2002 You should be able to 3A Differentiate the trigonometric functions sinx cosx tanx secx cscx and cotx 3B Differentiate polynomial functions 3C Differentiate exponential functions such as ex and ax a gt 0 3D The Rules of Differentiation i Apply the power rule the product rule the quotient rule and the chain rule to differentiate functions involving all of the above types ii Find the derivatives of functions given implicitly by implicit differentiation 3E Find the equation of a tangent line for a given function at a given point X0 Combine this and the concept of linear approximations to estimate values of fx for values ofx close to X0 3F Applications i Apply the concept of the derivative to physics problems such as those in Exercises 33 ii Deduce properties of a function f when you are given the graph or properties of its derivative f 39 Calculus Study Guide for Test 4 Revised December 2002 You should be able to 4A Differentiate exponential and log functions such as 611661 gt 0 and lnx and loga x a gt 0 Apply the power rule the product rule the quotient rule and the chain rule to these functions 4B You should know the statements and be able to apply the i first derivative test the ii second derivative test and iii L Hospital s rule 4C You should be able to find the following using techniques that involve derivatives i Critical numbers or points ii Relative max relative min iii Absolute max absolute min iv In ection points v Intervals where a function is concave up or down vi Limits using L Hospital s rule and by other methods 4D Solve related rate and optimization problems word problems 4E Approximate roots of an equation to a specified accuracy using Newton s Method 4F Antidifferentiate functions apply the indefinite integral 4G Given a direction field for a function draw an antiderivative of that function 4H Approximate the area under a curve using Riemann Sums 41 Use sigma notation to define a definite integral 4 Apply the Fundamental Theorem of Calculus Know the relationship between antiderivatives definite integrals and indefinite integrals


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