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Finding Functions Find differentiable functions f and g such that
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Calculus
- Sketching functionsa. Sketch the graph of a function that is not continuous at 1, but isdefined at 1.b. Sketch the graph of a function that is not continuous at 1, buthas a limit at 1.arrow_forwardFinding a constant Suppose Determine a value of the constant b for which lim xS2 f 1x2 exists and state the value of the limit, if possible.arrow_forwardDiscontinuous composite of continuous functions Give an example of functions ƒ and g, both continuous at x = 0, for which the composite ƒ g is discontinuous at x = 0.arrow_forward
- Linearizations at inflection points Show that if the graph of a twice-dierentiable function ƒ(x) has an inflection point at x = a, then the linearization of ƒ at x = a is also the quadratic approximation of ƒ at x = a. This explains why tangent lines fit so well at inflection points.arrow_forwardlim x → 0− g(x) lim x → 0+ g(x) Is g continuous at x = 0?arrow_forwardEven and odd functionsa. Suppose a nonconstant even function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An even function satisfies ƒ(-x) = ƒ(x).)b. Suppose a nonconstant odd function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An odd function satisfies ƒ(-x) = -ƒ(x).)arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning