114. Show that if ƒ is continuous, then f(x) dx f(1 х) dx.

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

A: Given,  ∫06 fx  dx=2

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

A:

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

A:

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

A:

Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

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

A:

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: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: 16 8 If f is continuous and f(x) dx = 10, find f(2x) dx.

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Q: 20 10 If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

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Q: 46. Find the values of a and b that make ƒ continuous everywhere. 4 - if x < 2 f(x) = ax? if 2 <x <…

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

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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: If f is continuous and f(x)dx=4, | xf(x?)dx=

A: We will find the value of the integral as following.

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

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

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

A:

Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: is Continuous and S' fldx=l6, find S xf(x*)a

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Q: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

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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: 35. Given that f(z) is a continuous even function, then A 0 B D

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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: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

A:

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

A: Given f1=2f4=7f'1=5f'4=3 f''x is continuous To find value of ∫14xf''xdx

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

A:

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

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

A:

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

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

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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: Find f(x) if f(5) = 0 and the tangent line at (x, f(x)) has slope x/x2+7. f(x) =

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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: 64 8 If f is continuous and f(x) dx = 18, find xf(x²) dx.

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

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Q: At what points is the following function continuous? 6x tan 3x y = x2 +2

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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.

A:

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

A: Given that: ∫09f(x)dx=4

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 19. If f is continuous and o f(x) dr = 20, find | #f(x*) dx af(r²)dr

A: given ∫09f(x)dx=20  and we need to find ∫09xf(x2)dx=?

Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

A:

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

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

A:

Q: Let (a) Show that f(x) is differentiable and that the derivative f(x) is continuous.

A: