Let y(x) be a continous solution of the initial value problem = Owhere f(x) = {1, 0 <= x <= 1 and 0, x>1} then find the value of y(2) y' + 2y = f(x) ; y(0)

Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

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Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

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Q: If f(x) = 1+/x, then f'(x) = -1 A 4/xV1+/x 1 B 4V1+x 1 4/x/1+Jx 1

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Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: find y(x) for x2y'-2xy=3x with y(1)=3

A: Given,         x2y'-2xy=3x  with y(1)=3

Q: 1. The Lotka-Volterra or predator-prey equations dU (1) = aU-UV, dt AP eyUV-BV. (2) dt have two…

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Q: x' y' 7x + 6y ||||

A: We have to find the value of x(t) and y(t).

Q: 13. f(x) = (x³ - Зx)(2x? + Зх + 5)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: to the equation (D²-1)y(x) = x'-x+1 y(x) = qe" +ce" +x-5x+1 -t yx)=ge" +ce --5x-1 - y(x)=qe'…

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Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: nctions f(x) = 3 + VI, 9(x) = x² – 3, %3D (a) (fo g)(x) (b) (go m)(r)

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Q: If fx)=5x-1, g(x)=1/x, and h(x)=g(fx)), then what is h'(0)?

A: Given that h(x)=g(f(x)) Using chain rule we get: h'(x)=g'(f(x))f'(x) We plug x=0 So,…

Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

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Q: 1 Suppose f(x) = v2x + 4 and g(x) %3D 2x + 5' (f o g)(x) (go f)(x)

A: We have to find function

Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))? and suppose that f(9) = 7, f(7) = 3, f'(7) = 14, f'(9) = 3…

A: topic - functions and derivatives

Q: Find the second derivatives, f"(x) of O a) b) f(x) = 2x² + e²² F"(x) = 2e² (4x²+4) F"(x) = 4+e²²(x²…

A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

Q: If given y'= f'(x), would would need to be given in order to find the +C

A: Given,          y,=f,x

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Solution:

Q: f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3).…

A: topic - functions and derivatives

Q: 12) Find a function f(x)with the f ollowing properties: 4 3 f'(x) = 2e2* –+ and f (1) = -2 %D

A: Given that: f'(x)=2e2x-4x+3x2 and f(1)=-2

Q: If f(x) = f'(2) 3x + 1 x + 1 then:

A: given  f(x)=3x+1x+1dxndx=nxn-1d dx(ab)=b(dadx)-a(dbdx)b2

Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

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