지2 2. If f is continuous and Sf(x) =. =6, evaluate (f(2sin@) Cos O d

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

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: 3. If f is continuous and | f(x) dx = 10, find af(x*) dr. Give proper reasoning.

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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: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: Suppose that h(x) has a continuous derivative h'(x), h(0) = -2, h(T/4) = 2 and tan(x)h'(x) dx = 4.…

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Q: Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f" is continuous. Find the value of *…

A: Use the method for integration by parts to solve the integral.

Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: 2. 지2 f f Š{(») = 6 , evaluate f(2sin6) Coso d@ is continuous and Sf(x)

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

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Q: 67. If f is continuous and f(x) dx = 10, find f(2x) dx

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Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: 10 If f is continuous and f(x) dx = -15, evaluate f(5x) dx. %3D

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Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

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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: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

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Q: Sx+2, if x 1 Value of k that will make f(x) continuous on (-0, 00) is ....

A: K=3 makes f(x) continuous.

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

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Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Q3) For what values of a and b are -x* +а, xsin + 1 0<xs y = bx3 + 2 , Continuous at every x ?

A: Explanation of the answer is as follows

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

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Q: '49 If f is continuous and f(x) dx = 18, find | xf(x?) dx.

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Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

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Q: and I = Jo x2+25)² 1 Let f(z) = ; (z²+25)² ;dx. Then f(x) is an even function,

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Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: To prove that given function is continuous. gx,y=xy3x2+y6,   if x,y≠0,00,              if x,y=0,0

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

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Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

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Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Iff is continuous on [a,b], and f(x) 20 then A True False ر VFX √f(x) dx = dx = √5 F(x f(x) dx

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Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: 9. If f is continuous and f(3x) dx. f(x) dx = 8, evaluate Answer:

A: Given:

Q: Where is f(a) not continuous?

A: Given:

Q: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

Q: Suppose that f(x) is continuous on [0, 9] and Fx) is an anti-derivative of f. If (0)=9 and F(9)=3,…

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Q: x²-1 for x# 1 - If flx) = show that flxx) is continuous at x = 1 x-1 2 for x = 1,

A: topic - limits and continuity

Q: 3. For what value of b, f(x) is continuous at every x? f(x) = {, x -2

A: Given that, fx=x         x&lt;-2bx2      x≥-2

Q: 86. If f is continuous and f (x) dx = 4, finc

A: Given that: ∫09f(x)dx=4

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

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Q: H.W Ex 4: if f (x) = where is f(x) continuous, and where it is discontinuous ?

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Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

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Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

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Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

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Q: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

A: