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

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

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

A: Given,  ∫06 fx  dx=2

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

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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: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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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: Given a function f with input that has the dimension [x] = L-M-T-1, such that [f(x)] = L-M, find the…

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Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

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

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Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

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

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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

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

A: given f is continuous and ∫09 f( n) dx = 2 we have to find ∫03 xf (x3) dx = ? we solve this by the…

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x<03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: f(x)dx converges then lim,f(x)=0

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Q: If f(x) continuous for x 2 0, and F(s) is defined by F(s) = | f(x) e *dx, where s > 0 Find F(s) for…

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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: 81 9 | If f is continuous and f(x) dx = 8, find xf(x²) dx.

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: Find dy/dx for f(x)=(Inx)x^2

A: Given:y=fx=lnxx2We need to find: dydx

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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

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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.

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Q: d rb If ƒ is a continuous function, what is the value of | f(x) dx? Explain your answer. dx

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Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

Q: - Use integration by parts to show that if f has an inverse with continuous first derivative, then…

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Q: 2.) f(x) = (x5 – 2x³ + 1) 3

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Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

Q: H.W Ex 2: Determine if the f(x) is continuous at x 3 ? at x-3 f(x) =- x²+2 at x 3

A: Given query is to find f(x) is continuous or not at x = 3.

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: 4 Suppose that f is continuous function such that |F( x) # x and 4 [(4x)dx = 3. Then fxf(4x² )dx =?…

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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: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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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: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

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: 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: 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: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…