What must be true in order forto be continuous at? Select all that apply.f(a) must be definedlim x->a f(x) existsf (x)O lim x->a f(x) = f(a)af must be differentiable at a

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Answered: What must be true in order for to be…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Advanced Calculus: Suppose f and g are differentiable functions on an interval I. Show that iff′(x) = g′(x) for all x ∈ I and f(x0) = g(x0) for some x0 ∈ I, then f(x) = g(x) forall x ∈ I.
For any R > 0, show f(a) is continuous at R when f(a) sqrt (x) is continuous on (0, +infinity) at R=b.
Let f be the function defined by f (x) = 3 6x. On which open intervals is f decreasing? 2 -2 3 © I< only There are no such intervals.
x² + 2x for <1 3 for a 1 f(x) = x³ + x²+x for 1
Sketch the given functions on a graph then answer the following questions: f(x)= 4-x for x < -2 f(x)= 2x+3 for -2 < x < 3 f(x)= -x for x > 3 1.) is this function continuous where x=3? Explain why or why not using the definition of continuity. (3 requirements that must be met) 2.) Where is the function right side continuous? 3.) Where is the function left side continuous?
is f (x) continuous at x = 10 Answer yes or no and explain why. See attachment
Find all points where the function f(x)=|x|^p is differentiable. How does the answer depend on the number p? Do I need to use the definition of differentiable, using limits, to show the points? Does it depend on p as p approaches infinity?
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x² 8x + 15, [3, 5] Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) f(b), If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) C =
Use interval notation to indicate where f(x) is continuous. SEE IMAGE

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What must be true in order for to be continuous at ? Select all that apply. f(a) must be defined f (x) lim x->a f(x) exists a O f must be differentiable at a O lim x->a f(x) = f(a)