If f(3) = −12 and f ′(x) = x2f(x) for all x, find f ″(3).

Q: b) Given h(x) = 3x² + 2x and f(x) =- Vx – 2, find (h • f) (x + 2)

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Q: 1 Find Vf if f = 2 /x²+y² +z?

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Q: If f(1) =1 and f (x) 2 3 for 1 <x < 3, how small can (3) possibly be?

A: We will find the smallest possible value of f(3) as following.

Q: Suppose that f(x) dx = 5. Calculate (4f(x) + 3) dæ-

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Q: Find f' (a) for 13x f(x) = 9x + 8 f' (a) =

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Q: Find the linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

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Q: Find a solution of by iteration for f (x) = x³ + x – 1 = 0

A: Given function is f(x)=x3+x-1=0 So we can write x3+x-1=0⇒x(x2+1)=1⇒x=1x2+1 Let ϕ(x)=1x2+1 Since…

Q: • Find f" (3) for f (æ) = x³ – 2x4 + æ³ + 2x? – 7x + 3. showing the steps in your process. - -

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Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

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Q: If we use the secant method on f(x) = x+x3+3 with X-2 0 and Xn-1 = 1, then Xn is_

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Q: 4.Find f (1) for f(x) = x² + 5x + 2

A: Given: f(x) = x2+5x+2.

Q: Find (fo g)(x). f(x) = 5x - 2, g(x) = – x² + 4x -1 O-5x2 +20x - 7 %3D | -25x2 + 40x - 13 5x +20x -7…

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Q: Find f"(x) for the functions x² +5x f(x) = ex b. f(x) = (x² – 1)e* a.

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Q: Find h' (2) if h(x) = 1n(x + √(x2 - 1)) h'(2) =

A: Given hx=lnx+x2-1

Q: (d) f(x) = ev4r+1 f'(x) = ,

A:

Q: For f(x) = 2x² + 5x+", find. 10 S(a +h)- f(a) if h +0. h

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Q: Suppose x E R. If x³ – 4x4 + 3x3 – x² +3x – 4>0, then x2 0. - |

A: Given that x∈ℝ. We have to prove the statement "If x5-4x4+3x3-x2+3x-4≥0, then x≥0" by using…

Q: find the interverse of the fuction f (x)= 2x + 3/x-4

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Q: ,if 0<x< n2 ) = }e** ,if 0 < x <n2 0, otherwise 8x+2 f(x) :

A: The range of x is (0 π^2), is it right?

Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

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Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: Given f(x) = x ^ 2 + 3x - 1 and g(x) = 2x + 1 ; what is (fog)(x)

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Q: If f(x) = ln ( v3x² +5 ), what is f'(x)?

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Q: Find the linear approximation of f(x) = x4 + 3x2 at a = 1.

A: We first find f'(a)=f'(1) f(x)=x4+3x2f'(x)=4x3+6xf'(1)=4(1)3+6(1)f'(1)=4+6=10   We now find f(1).…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: 8. For f(x) = -4x + 5, find the solution to f(x) = 41.

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Q: Let f(x)= 2x ; 0<x<1. Find E(3X+5)

A: Given, f(x)=2x   ;0&lt;X&lt;1

Q: For function f (x, y) = y2 x2 +1

A: Please refer the attached image for complete solution.

Q: Find the linearization L(x) of the function at a. f(x) = x4 + 6x2, a = −1

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Q: Find the domain of f(x) = ln(5x + 2).

A: fx=ln5x+2

Q: The derivative of f(x)= (x2+2x)(x²-2x) is a. 4x3-8 O b. x-4x2 с. none d. 3.

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Q: Find the inverse 0f             y =f(x)= x2, if x ≥ 0. Graph f and f -1.

A: A function g is the inverse of function f if for y=fx,  x=gy Inverse of x2:y=x2Replace x and…

Q: Find f'(a) for x2 f(x) = x + 6 at a = 3.

A: Given function :

Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7…

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Q: Given the function: 0 < x < f(x) = 5<x< n 2 п — х

A: Given that f(x)=x,    0&lt;x&lt;π/2π-x,  π/2 &lt;x&lt;πTo the plot the graph and find the fourier…

Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

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Q: Find f '(a) for f(x) = 3 − 2x + 4x2

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Q: Given f (x)= 2x +1 and g (s3)=x*+2x-1, find (I+g) (3).

A: (f+g)(x) = x2+4xexplanation is given below

Q: If FIX) is an antiderivative of x-2 + x1, then what is the value of F(1) - F(-1)? A) 3 (в) -2 -1

A: Solved below

Q: (B) Solve f(x) = x³ – 2x – 5 using Secant Method, correct up to 3 decimal places. Where xo=2 and x1=…

A: Given that fx=x3-2x-5  also x0=2 and x1=3 solve it using secant method

Q: With f(x) = 3x +1 and h(x) = 2x – 4, find (f o h)(5)

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Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

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Q: 3. For f(x) = x - 10, find the solution to f(x) = 5.

A: f(x) = x - 10 f(x) = 5

Q: Find the linearization at x = a. 1 f(x) = = 5 +3

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Q: The derivative of f(x) 4 (22 +17x) is O -4c (2a + 17) O -4r 2(2x + 17) O 4x + 68 O 4x 2(2x + 17) O 4

A: Here, it is given that f(x)=4x(x2+17x) We need to find the derivative of the function f(x).

Q: 5. For f (x) 3x 5 and g (x) 6 4x, find (fog) (x)

A: As per guideline we have to solve the problem

Q: If f(x) = x²+4 and h(x) = 3x – 4, what is f(h(x²+4))? O9x*+68 O9x* + 60 O9x*+ 48x2+ 68 Oex*+ 48x? +…

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Q: Find an antiderivative of ƒ(x) = 3x2 that satisfies F(1) = -1.

A: f(x)=3x2, F(1)=-1