Find A given that the function, f(x), is continuous at 6.f(x)={x2Ax−42x

Q: If f is continuous and f(x) dx = -1, find f(2x) dx.

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Q: Use the definition of the derivative, f'(x) = lim z+h)-(2) to findf' (x) where f(x) = x³ +1. h→0 O…

A: fx=x3+1

Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

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A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

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Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: Given a function f with input that has the dimension [x] = L-M-T-1, such that [f(x)] = L-M, find the…

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Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

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A: This question can be solve by taking approximation as x tends to a (more close)

Q: 4. Find the local maximum and minimum values of f, using both the First and the Second Derivative…

A: The given function is fx=x2x-1. Compute the critical points as follows.…

Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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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,…

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A: Given: fx=2x2+3  if x≤33x+B   if x&gt;3

Q: Find a value of x, if any, at which f(x) = Vx – 27 is not continuous.

A: f(x) = (x-27)(1/3) To find :- Value of x where function is discontinuous

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

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Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

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Q: Find values of x, if any at which the given function is not continuous. SU) = x2-25

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Q: h(x) = { 3-2 -2 if x≤-1 Cx² + 4x if x>-1

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Q: 8. If f is continuous and f(x) dx = 12, find f(2x) dx. 0.

A: Given f is continuous and ∫08f(x)dx=12

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

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Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: Consider the function g(x) =2x³ - 6x+3. The critical values for this function are and since these…

A: We have to find critical points

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: Determine whether the following statements are true or false:  1. ln(x')=[ln x]'  2. any continuous…

A: The given statement is,

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

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Q: Find values of the constants k and m, if possible, that will make the function f continuous…

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Q: g(x) = sec(x) %3D

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Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

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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: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

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Q: Find derivative of the following function by using formula f(x)= limit _f(a) - f(x) а -х a→X (3х-1)…

A: To find:

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: 2 2 If f is continuous on [0, 2] and / f(x) dx = 5, find the value of | f(x – 2) dæ.

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Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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Q: Find the value of constant c, if f(x) is continuous at x = 2 [cx? + 2x if x 2 -

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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.