(b) A function f(x) continuous at 0 and g(x) not continuous at 0 such that f(x)+g(x) is continuous at 0.

Q: Let g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

A: Explained below

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

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Q: Let f and g be differentiable functions such that f'(0) = 3 and g' (0) = 7. If h(x) = 3f(x) - 2g(x)…

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Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

A: Here I am attaching image so that you understand each and every step.

Q: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: 1. Examine the continuity and differential possibilities of function f (x)= |x² – 1| in x= 1.

A: Given To check for continuity at x=1 , we find the limit to the left and right of x=1

Q: 1. Find the value/s of b such that the function f is continuous everywhere. x3 + 2, x 0

A: In the question we have to find value of b.

Q: Н56: | Let g : [-1, 1] → R f(x) = x2 · g(x) für x € [-1,1]. f :(-1,1] → R f'(0). be a bounded…

A: g:-1,1→ℝ be a bounded functionf:-1,1→ℝ be defined by fx=x2 g(x)

Q: Let g(x) be a differentiable function, and let H(x) = g(tan(x)) + cos-(g(x)). Determine an equation…

A: our objective is to find the derivative in terms of g and g'.

Q: If f isa differentiable function satisfying f(0) = 0 and f (0) = 2, then 1- cos( f (x)) lim x-0 A) 0…

A: The given limit is, limx→01-cos(f(x))x2. Note that, the given limit is of the form 00. Apply L…

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: What is the minimum value of F(x) = -4 sin

A: Answer and explanation is given below...

Q: If f is a differentiable function on an interval containing a point xo, then its linearization at xo…

A: Let f be a differentiable function on an interval containing a point x0 ∈ a,b, then the linear…

Q: 2. Let f : R → R be a differentiable function. Show that the function f', the derivative function of…

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Q: x +1 1. Let f(x) = prove that f is continuous at 0. x – 1 -

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: 5. Find the exact absolute maximum and absolute minimum values for f(x) cos(x) + sin (x) on the…

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Q: 2. State the definition of a C function f from R" to R. State the definition of the linearization…

A: Respected student, by Bartleby policy we have to solve only 1 problem if multiple problems are…

Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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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: If f(x) =0 at x=c then f has either a minimum or maximum at x=c. If a differentiable function f has…

A: To Determine: true or false                           1) if f'(x)=0 at x=c then f has either a…

Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…

A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…

Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: f(x)= X-I x=1 √x-1 X = 1 1123 -s continuous at x = 1?

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Q: Consider the function f(x) = x – 3 ln(x) on the interval 3 The absolute maximum value is and this…

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Q: x2- 1 -1Sx<0 1- If f(x) 1 x=0 is it continuous at x=0 %3D 2х 0<x<1

A: Here the given function is  f(x)=x2-1if -1≤x&lt;01if x=02xif 0&lt;x≤1 We need to find weather the…

Q: f(x+h)-f(x) For f(x) = x- + 2x, use the definition of the derivative f'(x) = lim h→0 to find f'(x).…

A: Using the definition of derivative formula,

Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

Q: 4. The graph of f'(x), the derivative of a function f(x), is shown at right. Which of the following…

A: f(x) is continous at x=a f(x) is also differentiable as f'(x) exists at x=a ; Since f'(a) is not  0…

Q: The function f is continuous for all real numbers and the graph of its derivative function f' is…

A: Given The graph of the derivative of a continuous  f

Q: The derivative of the function f(x)= 1- In xr is: -1 -x f'(x) = f'(x)= 2x/1- In x 2/1- In x O This…

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Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

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Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

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Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

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Q: f(x)={x2−3x     x≤5          2x            x>5 (a) Is f continuous at x=5  ? yes, or no (b) Is f…

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Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: Consider the function y = g(x)= -x² + 3x +2. Compute g(2). Use the limit definition of the…

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Q: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

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Q: (a) Give an example of a function f that is differentiable at 0 but whose derivative f' is not…

A: Darboux theorem: Let, f is differentiable functions on [a, b] then for every k with…