Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0

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

A: Explained below

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: Suppose that a continuous function g satisfies: 3 g(x)dx = 6 and | 9(27)dz = 9. 0, | z9(3z*)dz. Find…

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Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

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Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: If f(x) is continuous at x=a , then f(x) is also differentiable at x=a.

A: " If F(x) is continuous at x=a then f(x) is differentiable at x=a." The condition for the function…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: Use the Intermediate Value Theorem to show that f(x) = cos^−1 (x) − e^x has a zero in the interval…

A: The Intermediate Value Theorem: If f is a function which is continuous at every point of the…

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: Let f(x) be a continuous differentiable function that f(x)- 4 satisfies lim =D5 %3D x3 x-3 Which…

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Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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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: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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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: Show that the function is continuous. f(x) = cos(x 2)

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Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: 2. Determine if a function f : [0, 27] → R defined by f(x) = sin 2n is continuous.

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Q: The limit of f(x) = sin(x) as x approaches t is O T/x n/2

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Q: Let f be the function defined by: sin x, x 2 - For what values of x is f NOT continuous?

A: Given function is: fx=sinxx&lt;0x20≤x&lt;12−x1≤x&lt;2x−3x≥2

Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: Is g(x) = ln( x2+2 ) uniformly continuous on the interval (−∞,∞)?

A: given function is                                                        g(x)=lnx2+2 log is defined…

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

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

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Q: (d) A function not continuous at 0 such that (f(x))4 is continuous at 0.

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Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

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Q: Show that the function below is continuous at x 0 (cos x-1 f(x) D if x<0 5x, if x20

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Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: Determine the set of values of the continuous function defined by the formula: T COSX b) g(x)= sin 6

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Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: Let f be a continuous function such that f (x) dx 5 and 6° | f(x) dx = 3. What is the value of |…

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Q: Determine if f is continuous at the indicated values. x = 0 f(x) = 1 sin x x + 0 a) x = 0. ? b) x =…

A: Given

Q: Find a nonzero value for the constant k that makes the function (tan(kx) x < 0 f(x) = Зх + 2k?, x 2…

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Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

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Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

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Q: function, that is 0 everywhere except at t=0, is know as:

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Q: Determine the set of values of the continuous function defined by the formula: a) f(x)=cos sin

A: Given that fx=cosπ3sinxgx=π3sinxsinx is continuous in x∈-∞,∞gx is also continuous in  x∈-∞,∞.Range…

Q: If f(x)= 2- cos(x) sin(x) , then the absolute minimum of f on the 3T is: interval O 13 O 0 P 2/2-1 O…

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Q: B) Show that f(x) sin for x * 0. for x= 0. is not continuous.

A: