WRITING ABOUT CONCEPTS
Finding Functions Find differentiable functions/and g that satisfy the specified condition such that
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Calculus: Early Transcendental Functions (MindTap Course List)
- Graphical, Numerical, and Analytic Analysis use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods.arrow_forwardContinuity and the properties of limits: show a function is continuous at aarrow_forwardUniqueness of limits Show that a function cannot have two differentlimits at the same point. That is, if limxSc ƒ(x) = L1 andlimxSc ƒ(x) = L2, then L1 = L2.arrow_forward
- lim. 3cosx x—> infinityarrow_forwardThink About It Consider the functionsf(x) = x + 2 and f −1(x) = x − 2. Evaluate f( f −1(x))and f −1( f(x)) for the given values of x. What can youconclude about the functions?arrow_forwardlim f(x) as x approaches infinity lim f(x) as x approaches negative infinityarrow_forward
- True or false. if false, correct statement. if true, explain why. a. if a function, f, is continuous at a point c, then f is differentiable at the point c. b. if a function is concave down on its domain, then it will have a relative maximum. c. The derivative of a sum is the sum of its derivatives. d. the derivative of a function, f(x), is equal to limh->0 (f(x+h)-f(x))/h for all x values in the domain e. if f has an absolute minimum at c, then f'(c)=0arrow_forwardTheory and Examples1) Once you know limx-->a+ ƒ(x) and limx-->a- ƒ(x) at an interior point of the domain of ƒ, do you then know limx-->a ƒ(x)? Give reasons for your answer 2)If you know that limx-->c ƒ(x) exists, can you find its value by calculating limx-->c+ ƒ(x)? Give reasons for your answer. 3)Suppose that ƒ is an odd function of x. Does knowing that limx-->0+ ƒ(x) = 3 tell you anything about limx-->0- ƒ(x)? Give reasons for your answer. 4)Suppose that ƒ is an even function of x. Does knowing that limx-->2- ƒ(x) = 7 tell you anything about either limx--> -2- ƒ(x) or limxS-->-2+ ƒ(x)? Give reasons for your answerarrow_forwardEvaluating composition of function use f(x)=2x3 and g(x)=4x2 to evaluate the expression. (a) f(g(0)) (b) g(f(0))arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning