69. Let f(x) = x. Find an interval [a, b] such that 3 f(x) dx and If(x)|dx : 2

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

A: Given,  ∫06 fx  dx=2

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

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

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Q: If f is continuous and f(x) dx = 8, find xf(x?) dx. %3D

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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: 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…

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

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Q: 9. If f is continuous and | f(x) da = 3, find æf(x?) dx.

A: We have to evaluate the given definite integral using the other definite integral.

Q: Let f be a continuous function such that -6 [', f(x) dx = 9. What is the value of -3 f(x) dx = -10…

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

A: Explained below

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

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Q: If; of t = x then at t=1 is (Note that these functions in N) dx

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Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x&gt;3 we have to check the given function is…

Q: 64 8. f(x) dx = 14, find xf(x?) dx. If f is continuous and %3D

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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. Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin z for x €R is…

A: In the question given that we have to solve any one of them. Let us solve the first one.

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: Let f be a continuous function such that | f(x) dx = -10 and | f(x) dx = 9. What is the value of…

A: Given: Let f be a continuous function such that ∫52fxdx=-10 and∫-25fxdx=9. To Find: What is the…

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

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

A:

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

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

A:

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

A:

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

A:

Q: 2. For which values of a is f(x) differentiable on R?

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Q: 26. Assume that f is continuous and f(x) dx = 12. Find %3D f(x³)x² dx

A:

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

A: Given:

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: Where is f(x) = e* continuous?

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Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

A:

Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,…

Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

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Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: Give the linear approximation of f(x) = x sin(nx2) at x = 2. Use this to estimate f(1.98)

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Q: 87. If f is continuous and f(x) dx 10, find f(2.x) dx. %3D

A:

Q: For what values of the constant c is the function f continuous on (-o, )? Show your work. S ex + 4,…

A: Please see the answer below

Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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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: For which  x value(s) is the function  f ( x ) = sin ^− 1 ⁡ ( 2 x )  defined and not differentiable?

A: Given that the function is       f(x) = sin-1(2x)  Here we have to find those values of x, in which…

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

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

A:

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

A: