+ 3x - 6x if xs-2 if x>-2 A) Check the continuity of the function f(x) at x =-2 f(x) =

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Q: Use the limit definition to calculate the derivative of the linear function. f (x) = 7x − 9

A: Plug the given function in the limit definition of the derivative

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Q: Use the chain rule to find the derivative of f(x)= 5e^-9x^3-6^x^7

A: Given query is to find the derivative of the expression

Q: Discuss the continuity of the function

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Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

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Q: Use the limit definition of a derivative to find f'(x) f(x)=3x^2+2x-1

A: The formula for the limit definition of derivative is as follows: f'(x)=limh→0f(x+h)-f(x)h

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A: The given function f is,

Q: Discuss the continuity of the function on the closed interval.

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Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

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Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

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A: For function g(x) to be continuous on -1 limx→-1-g(x)=limx→-1+g(x)=g(-1)…

Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 ax2 - bx + 1 4x…

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Q: Use the limit definition of derivative to find f (2) if f(x) = V2x + 3.

A: Use the formula for the derivative from limit defination.

Q: Find the values of a and b that make f continuous everywhere. x² – - 4 if x < 2 X - 2 f(x) ax2 - bx…

A: Please refer the attached image for complete solution.

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

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Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: Let f (x) = 2x² + 1. Use the limit definition of the derivative to find f'(x) %3D

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Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: 3x if x S -2 3. If f(x) x* - 1 if -2<x<2 = 3 if x 2 2 Discuss continuity at x = 2 and x = -2

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Q: Find the value for k so that the function will be continuous at x = 1. - 5x2 - 30x + 35 - 10 if x <…

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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Q: Find the value of a and b that will make the function continuous. for x 1/2

A: The function f(x)=1x,        for x&lt;-1ax+b,  for  -1≤x≤121x,         for x&gt;12. We have to find…

Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

Q: use the limit definition of the derivative to show that the derivative of  f(x)=x^2+9x is…

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Q: Find the values of a and b that make f continuous everywhere. x² – 4 х — 2 ax2 – bx + 3 4х — а + b…

A: The given function is: f(x)=x2-4x-2            if  x&lt;2ax2-bx+3if  2≤x&lt;34x-a+bif…

Q: R(x)= ex-1

A: Domain of a function is the all possible values of x such that f(x) exists finitely. for f(x)…

Q: Explain why f(x)=3x^2+1 is continuous at x=-2

A: Consider the function  f(x)=3x2+1

Q: Q3: Choose A or B (one only) if xs-2 if x>-2 A) Check the continuity of the function f(x) at x = -2…

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Q: Use the limit definition to find the derivative of the function. f(x) = 3x2 + 8x f'(x) =

A: From the limit defination the derivative of a function formula is f'(x)=limh→0[f(x+h)-f(x)]/h

Q: x+4 if x2

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

Q: Use the limit definition to find the derivative of the function. f(x) = x² + 5x – 5 - f(x + h) – f…

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Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(a)