continuous at (C

Q: Evaluate the function shown, where ƒ is continuous on [3, 8], ƒ(3) = 4,and ƒ(8) = 20.

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Q: (0,1). Prove the following functions is uniformly continuous on sin x f(x) =

A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

Q: Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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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: For what value of b is

A: The given function is continuous for all x<0 and for all x>0, because it is a polynomial…

Q: Find the value of c which satisfies the Mean Value Theorem with the given f (x) =e*, [0,1].

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Q: If f(x) is continuous at x = c then f'(c) exists. True False

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Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

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

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Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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Q: Suppose that f(1) = 3, f(4) = 5, f '(1) = 4, f '(4) = 4, and f " is continuous. Find the value of xf…

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Q: iii. is continuous at a provided g(a) # 0.

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

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Q: Let X be continuous with pdf f(x) = 3x² if 0 <x< 1, and zero otherwise. Find: (a) E(X). (b) Var(X).…

A: The pdf of X is given by f(x) = 3x2 if 0 &lt; x &lt; 1 Note : According to our guidelines we are…

Q: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

Q: 25 If f is continuous and f(x) dx = 12, find xf(x?) dx.

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Q: If f(3) = 15, f' is continuous, and I f'(t) dt = 24, what is the value of f(4)? %3D

A: In this question, f is a primitive function and we have to find f(4). So I am providing the…

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

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Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

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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: True or false: if f(x) is continuous at x =a, then f(x) is differentiable at x =a.

A: We have to determine the given statement as true or false.

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: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Find the values of x where the tangent line is horizontal for f(x) = 3x- 2x-9. %3D O A. x-0, x= ОВ.…

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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: Use the first fundamental theorem of calculus to find F'(x) F(x) = cosr' dt

A: In this question we have to find F'(x).

Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

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Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

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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: - For what value of b is Sx, bx?, x2 -2 x<-2 х, g(x) = continuous at every x?

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Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

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

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Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

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 ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

Q: Give a formula for f(x) given that f is continuous and 2 x +x* + 2 = f (t) dt t+ 2

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Q: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

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

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