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: (x^2)y''-2xy'+2y=0; y(1)=4, y'(1)=7   Find particular solution that satisfies the given condition

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Q: If f(x) = (5x +7)°, then the value of (f-1 (x))' at (f(-1),-1) is

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Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

Q: f(x)= (x+2)² (x - 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

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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: ax? If f(x) = if x > 1 then the bæ + 2 if a<1 values of a and b such that f is differentiable on…

A: For function to be continuous

Q: LET F(x) = f(x8) AND G(x)=(f(x)) 8 F(a) = 3 F'a = 7 F' (a 8) = 4 a 7 = 11 FIND F' (a) = 7 AND G' (a)…

A: 2.

Q: Suppose that you have $11,000 in a rather risky investment recommended by your financial advisor.…

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Q: 16) g(x) = 4x - 5 s(x) = x' + x² Find (g + f)(-2)

A: Given,      g(x)=4x-5      f(x)=x3+x2

Q: f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1,…

A: Given : hx = fgxpx = fx·gxqx = fxgx

Q: if f(x) = 3x+4 over 4x+3 then f'(x)=?

A: Given: fx=3x+44x+3 To Find: f'x=?

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: Let 2² + y? = 1 and y(0) = 1 Then y'(0)= none of the listed here 1 -1

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

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

Q: If f(x) = f'(x) = f'(1) = 7x + 5 6x + 2 3 find:

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Q: If y" = 1 (x + 1)² y(0)=2 y'(0) = 1 then y'= and y=

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Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

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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: (b) If f (2) = (249 + 8) e8ɛ, then at how many points the function f (2)is not differentiable? (c)…

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Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: If f(x) = 5x4 – 2x3 –x² + 3x – 1, then | f'(0) = d2 ;f(0) = dx f"'(x)= d4 ¡f(x)= dx

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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…