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

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

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Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

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Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

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Q: Show that [x² +x + 1, x 1 Sketch the graph of f.

A: A function f(x) is said to be continuous at a point x=a if its left hand and right hand limits exits…

Q: 5. Use the definition of the derivative to find f'(x) if f(x)== x-÷ (i.e. ƒ(x)= . (i.e. f(x +h)-…

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Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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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: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: Find the instantaneous rate of change of each function at the given x-value. Use the form lim…

A: a) Given that…

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

A: This question is about finding derivative about a point .

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x&lt;03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: Determine if the function the following function is continuous 2x for x <4 a) Lim f(x) wbere f(x) =…

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Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: Determine for what values of x the function f(x) = 32 ln(x) − x^2 + 6x − 5 has a tangent line with…

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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: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

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: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: For x > 0, find f'(x) where f(x) = x*¯+3) via logarithmic differentiation. Show all ur work.

A: Topic:- application of derivatives

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

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Q: The first derivative of a continuous function y=f(x) is given, find y’’ and then sketch the general…

A: Our objective is to find y'', and then sketch the general shape of the graph of  f.

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: Determine whether the function 1s differentiable. at, X=1$ then sketch a graph of ysf (x).

A: Step:-1 Given that fx = xif x≠12if x=1 And Right , left derivatives are respectively,   f+' 1…

Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: 1. Let f(x) =1. Using the limit definition of the derivative, find f'(x).

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Q: Let f(x) = /3x + 4. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim х — а…

A: The derivative of f at x = 1 is

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: ifx 1

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Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

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Q: x+4 if x2

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Q: 20. Determine the following function if continuous at 2x g(x) = \72 – 4x + 3 . ; at x = -1 A.…

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Q: Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

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Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

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Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…