For which value of a is this function continuous? Please use exact values. { ах — 1 x > 3 f(x) = x2 x < 3 a =

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

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Q: f(x) = 9x² - 4 at x = 1

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Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: Find the values of a and b that make the following piecewise defined function both continuous and…

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Q: f(x) = at x = 1 X-2

A: A polynomial function is always Continous in its domain

Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

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Q: List the x-values where the function is not continuous: f(x) = -x+ 3 if ex if if 3 – x x < - 3…

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Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: Determine whether the following function is continuous at the given point x = 6: x2 8x + 12 - x + 6…

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Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: f(x) = x2 -4x-2 at x = 1 %3D %3D

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Q: Find the number c which will make the function continuous on (-00, 00). x< 2 f(x) = x+ c, x22

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: f(x) at x = - 3 X-3

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Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

Q: Which of the following functions are continuous? Why do you think they are continuous?

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: Is the functionf graphed below is continuous at x= -1? Choose the appropriate reason that justifies…

A: Continuous at x=-1, as limit is equal to f(-1).

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: The graph of the derivative, f'(x), is given. Determine the x-coordinates of all points of…

A: The graph of first derivative is,

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = x3 2.F(x) = = Vx3 - x

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Q: Determine if the given function is continuous at a given value of x.

A: This question is related to limits and continuity, we will solve it using given information.

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Determine the open interval(s) in which f(x) = 2x3 – 6x² is increasing or decreasing. Also, ocate…

A: Given        fx=2x3-6x2

Q: 1. (x) = 3x + 2x +1 at x = -2

A: f(x)=3x2+2x+1

Q: The function is continuous from the right at x = 2. Select one: True False f(x) = x+ 2 x². x < 2 x22

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Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: For what value of the constant c is the function f continuous on (-∞, 0)? if x 5 C = Need Help?…

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Q: find the value of c that make the function continuous

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: If f is even and differentiable function, the x = 0 is a critcal number of f. True or False

A: Known fact: For even differentiable function, 0 is a critical number.

Q: 1 Use the limit definition of the derivative to find f'(x) if f (x)= 10x

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Q: Suppose the derivative of a function fis f'(x) =(x + 1)°(x÷ 3) xH6) On what interval is finereasing?…

A: For f to be increasing, f' must be positive.

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Use the definition of a derivative to show that if f(x) = 1/x, then f'(x) = -1/x². (This proves the…

A: Given: fx=1x

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)