iff.g,h becontinuous functions on [0,a]such that and sh(x)-4h(a - x)=5, then provw that f(x)g(x)h(x)dx =0. ||

Q: Suppose that f(x) is a function, whose derivative is f '(x)=(1 + cos x)(e* – 1)(x – 2)²(x – 3). At…

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Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: 10. Iff(x) = Vx find f (4). 11. Use the limit definition to find the derivative of f(x) = x² –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: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

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

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

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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: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

A:

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

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

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Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…

A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…

Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

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Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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

A: We will use the definition of an even function and properties of definite integrals to find the…

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

A: Solution is in step 2

Q: a) For the function f(x) =1–3x² , find f'(a) at a =-1 by using the definition of derivative. (a + bx…

A: Integration means addition. It is used for adding a continuous function that cannot be added by…

Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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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?

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Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

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Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

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Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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

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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: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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

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Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

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