4. Let f(x) x² + cos(Tr). f&)= Qx -Tsin(Tx) (a) Use Newton's method to find the root of f(x) with x1 =-1/2 and within a tolerance of 10-4 (b) Use Newton's method to find the root of f(x) with x1 = 3 and within a tolerance of 10-4. (c) Explain why Newton's method fails with an initial guess of x1 =0.

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

A:

Q: Find the iterative scheme for the root of equation cos x- 3x+1=0 by Newton-Raphson method. O a. None…

A: Newton rephson method problem....

Q: What is the value of x in the 4th iteration of Newton-Raphson method with initial guess of x=2. F(x)…

A:

Q: 10 Show that the equation 2x+e" - 2 =0 has a root between x 0 and x= 1. Using the Newton- Raphson…

A:

Q: 5. Use Newton-Raphson method to find solutions accurate to within 10-2 for x - cos x = 0 on [0,…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 1. Calculate for one real root of tan x = 4x with 0 = 1.2 co up to four decimal places using the…

A: We need to find one real root of  tanx=4x with initial guess x0=1.2 upto four decimal places using…

Q: 1. Calculate for one real root of tan x = 4x with xo = 1.2 up to six decimal places using the…

A:

Q: 2- Find the positive root of f(x) =xe - cos (x) with an error tolerance -0.005% by using a) The…

A: (Solving the first three subparts as per our guidelines) Solution: The function is fx=xex-cosx Error…

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

A:

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0]. If we use…

A:

Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

A:

Q: 1. Calculate for one real root of tan r 4x with ro 1.2 up to four decimal places using the…

A:

Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

A:

Q: 1-Show that the function defined by the base harmonic function f(x, y) = ex cos 4y

A: As per our expert guidelines we are allowed to solve only one question. kindly repost others. thank…

Q: 2. Determine one real root of 8 (sin x) e¯* – 1 = 0 with xo 0.30 using three iterations of…

A:

Q: The approximation of the root x* of the function f(x) = x*e* – 1 accurate to within 10-2 using…

A: To find  The approximation of the root of f(x) accurate to within 10^(-2) using Newton's method.

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

A:

Q: 15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation…

A: a. Let fx=ex We know that the Maclaurin series is fx=ex=1+x+x22!+... The remainder term is…

Q: 4) f(x)=- - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 cos(3x) +... 12

A:

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

A:

Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

A:

Q: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

A:

Q: () = 2 + Solve the initial value problem : f'(x) = cosx + sec?x, %3D

A: As you post multiple questions we only solve first question only.

Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

A:

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

A:

Q: 7. (a) Use Newton's method ONCE with an initial guess of ro = 0.1 to find an approxi- mation to the…

A:

Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

A:

Q: 2. Determine one real root of 8 (sin x) e¯* – 1 = 0 with xo = using three iterations of Newton-…

A:

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

A:

Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 1. Calculate for one real root of tan x = 4x with xo 1.2 %3D up to six decimal places using the…

A: Ques : tanx=4x f(x) = tan(x)-4x f'(x) = sec2(x)-4 x0 = 1.2 By Newton Raphson method xn+1…

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

A:

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: 10. Show that :" + 42' + 8z = 0 if z = e-# (sin 2r + cos 2r). 11. If f(r) = rª and g(r) = rª, then…

A:

Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (3)…

A:

Q: =1+ cos (x) x2 + 12x + 20 -dx 1 + cos² (x) 0. At what value of t does the local max of f(t) occur?

A: Given that f(t)=∫0tx2+12x+201+cos2 xdx To find the local maximum of f(t) at t:

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: 2) If the Newton-Raphson method is used to solve the equation f(x)=x²e*cos (2x) and x = 0.75, then…

A:

Q: Given that f(x) = V3 cos 5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a…

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

A:

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A:

Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.