e the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the lues.

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

A:

Q: V4 + 3f(x), where f(1) = 7 and f'(1) = 4, 62. If h(x) find h'(1).

A:

Q: Use Exact, Then solve (1 = In(x) +)) = (1 – In(x))y`

A:

Q: Va - 2 find: Va + 2 If f(x) = f'(x) = f'(2) = %3D Submit Question

A:

Q: Show that P2(x) = f(a) + f'(a)(x − a) + c2(x − a)2 for each value of c2 satisfies the requirements…

A:

Q: f(x) f (x) a (x) g' (x) 1 0 -4 -3 -2 2 -4 -3 -3 3 -4 4 5 14 4 6. 17 27 31 h(x) = xf(x)+g(2x – 5)…

A: to find h'(3)

Q: If h(x) = and f(1) =2, f(1) =3. g (1)=-3, g'(1) = -2, compute h'(1) f (x) g(x) B h'(1) -- 54 54…

A: Given that the function hx=fxgx   and f1=2 , f'1=3 , g1=-3 , g'1=-2   .

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

A:

Q: Find g' (8) given that f(8) = – 3 andf 8) = 6. %3D

A:

Q: Find g(1) if f (1) = 0, f'(1) = 2, and (fg)'(1) = 10.

A: The value of a function is obtained by substituting a value from its domain in the function…

Q: Find y' and y". y' y" = y = (²+ √x)³ 3

A:

Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

A:

Q: Find f'(x) and find the values(s) of x where f'(x) = 0. f(x) = (2x – 21) (x² + 18) f'(x) =O

A: Given function, f(x)=2x-21x2+18 Multiply the function, f(x)=2x3+36x-21x2-378 For differentiation,…

Q: g'(2) = g(x) = x + 4

A: dxndx=nxn-1g(x)=x+4x2g(x)=x+4x-2

Q: If g'(x) = Vx -+ Vĩ, g(0) = 2, then g(1) = ? %3D %3D Answer:

A: Topic- integration

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: Find g' (3) given that f(3) - 5 andf' (3) Enter the exact answers. (a) g(x) = 4x² – 3f(x) g' (3) = i…

A:

Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

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: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

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).…

A:

Q: '(x) = 7ex − 8x; f(0) = 16

A:

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

A: