Find S f(x)dx if f(x) = [2 for x<2 [x for xz2

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

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Q: b) I =f- x(1+(In x))

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

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: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: Find F(s). F(s) = £{t¹8e-4tz X

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Q: If f(x) = and g(x) = Vx, then the derivative of f(g(x)) is -VE (A) ( + 1) (B) -(x + 1)- -2x (C) ( +…

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Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: Let f(x) = 3x+ 4x. Evaluate dy when x=2 and dx=0.1

A: Given that fx=3x2+4x To evaluate dy when x = 2 and dx = 0.1.

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: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

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

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Q: (B) Verify the Mean Value Theorem for f(x) = ln(4x + 1) on | 0,

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Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

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Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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

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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: Suppose f(x) = In(x³ + 5x + 7). df Find the derivative dx f' (x) =

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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: Let f(x) = 3x² + 4x. Evaluate dy when x=4 and dx=0.1

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

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Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

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Q: '49 If f is continuous and f(x) dx = 18, find | xf(x?) 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: 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: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Find the values of x where the tangent line is horizontal for f(x) = 3x- 2x-9. %3D O A. x-0, x= ОВ.…

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Q: In(4x Given f(x) = the derivative f'(x) is 4 1 4x 1 4x O 4 O z4z

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Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

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: nd the derivative of the functionf(x) = v 5x+6 using the limiting proces A) S'x)= - 2 5x+6 Sx) = 2…

A: We are asked to find the derivatives of the function using limiting process.

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Compute f -f(g(x)), where f(x) = x° and g(x) = 8x – 1. dx -f(g(x)) =| dx

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Q: 3 xf(x2)dx df(x) dx = -9, find If f is continuous and 0

A: f(x) is continuous

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: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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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: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

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

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Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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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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