7. Use Newtons method with the given X(0) to compute X(2) for each of the following nonlinear systems: (a) sin(47x122) – 2x2 – x1 = 0 - 1 ) (e2r1 – e') + 4e'a} – 2e'x1 = 0 X(0) = (0,0)* (b) xỉ + xịx2 – x1x3+6 = 0 e#1 + e*2 – x3 = 0 x3 – 2x1x3 = 4 х0) — (-1,-2, 1)*.

Q: Let H(x) = F(G(x)) and J(x) = F(x)/G(x). Suppose F(4) = 9, F'(4) = -7 G(4) = 3, G'(4) = 0 G(-6) = 4,…

A: Given H(x)=F(G(x))H'(x)=G'(x)*F'(G(x))J(x)=F(x)G(x)J'(x)=G(x)F'(x)-F(x)G'(x)G2(x)

Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5. We have to find the solution of given…

Q: x' = (C )x ´sec X + 0, 1

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 4, f(4) = 2, f'(4) = 8, f'(9) = 4 Find…

A: Given:   F(x) = f(f(x)) and G(x) = (F(x))2

Q: 2. Use derivative rules to differentiate each of the following function: a) y = V b) y 4x³ +…

A:

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)?

A:

Q: In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the…

A:

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = -2x³ f(x)=

A:

Q: The general solution of x' = 2x + 5y and y' = -2x - 4y

A:

Q: If h(2) = 4 and h'(2) = π, find g'(2) where g(x) = 2x h(x) + cos(x)

A: To find out the derivative of the given function.

Q: (1) If f(x) = = x², then f'(x)= (3) If h(x) (2) If g(x) = - 6x5, then g'(x) = = 1 = I then h'(x) =

A: formula used is   dxndx=nxn-1d dx(constant)=0

Q: oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in…

A:

Q: We have an unknown function f(x) which satisfies    f''(x) + f'(x) -2f(x) = x2 The first term is the…

A:

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: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

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

A:

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: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

A:

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: a)Use the second derivative test to determine whether the function has a local maximum or local…

A:

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: Find the nonhomogeneous ODE whose general solution is y=c₁(x+1) ³+c₂(x+1)3³+x-1. (x + 1)² y" + (x +…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

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)…

A:

Q: Find g' (4) given thatf(4) = - 5 and f'(4) = 10. Enter the exact answers. (a) g(x) = 5x – 4f(x) g'…

A: (a) The function is g(x)=5x2-4f(x)  f(4) = -5 and f '(4) = 10

Q: x' - (; )*+()- 1 3 X + \3, %3D 1 1

A: