We say a function f is even if f(x)= f(-x) for all x in its domain. We say f is odd if f(-x)= -f(x) for all x in its domain. Suppose f is differentiable everywhere and is even. Explain why f'(x) is odd.

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We have to find the derivative of the function, using dxndx=nxn-1

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

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: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

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

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

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Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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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: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Give an example of a function that is continuous but differentiable at x=2

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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: ) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D (3 Marks)

A: Answer - definition of derivative f'(x) = lim h tends to 0 ( f(x+h) -f(x) ) /h

Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

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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: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

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 f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

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: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

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Q: Find f '(x) for f(x) = In x - %3D www f '(x) = www

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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: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

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

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Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

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: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

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Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: Suppose f is differentiable with f(0) = 0 and 0 0.

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Q: f(x)=√√x at x = 7

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Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.