Find a continuous particular solution to the initial value problem (1+x²). + 2xy = f(x), y(0) = 2, dy dx where f(x) is the piece-wise defined function Sx, 0, f(x) = when when 0 ≤ x < 1 x ≥ 1

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: Consider the function Compute f"(x). X = 66²⁰ - f(x) = -3t²- f"(x) = -4t+ 3 dt.

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Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

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Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

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Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

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Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: 14. The function g is defined as g(x) = 3x + | (1+?) dt. What is the value of g'(2)? %3D (A) 20 (B)…

A: The given function is- gx=3x+∫1x21+t2dt Then evaluating the integral-…

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

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Q: = 4+ J₁ Find F'(x). 2t² + 1 t² + 3 dt.

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Q: Q.5 Show that both of the functions f(x)=(x-1)" and g(x)=x' – 3x +3x-2 have stationary points at x =…

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Q: 2x 1 Let f be the function defined by f (x) = | dt. Find an expression (2t – 5)6 - for f'(x).

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Q: An equation of the line tangent to the graph,of f (x) = x(1– 2.x)' at the point (1,–1) is D y = 7x…

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Q: Find the derivative of y=x√x + 1. 1 dy = 2(x+1) ³ + √² ž √x+1 dy dx = dy dx dy √x+1+ dx = x √x+1 = =…

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