31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: Compute for a real root of Sin Vx – x = 0 using three iterations of Fixed-Point Iteration - Method…

A:

Q: 4. Determine the root of F(x) = 7 sin(x)e-x – 1 using secant method with 3 iterations glven Xi-1 =…

A:

Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

A:

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

A: Let t =-x >0. Then the differential equation       4x2y''-4xy'+3y=sinln-x becomes…

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Find a root of the equation 3x + sin(x) - e* = 0 using Newton Raphson Method. Consider initial guess…

A: Let fx=3x+sinx-ex Then f'x= 3+cosx-ex Given that x0=2·500

Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

A:

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: 1. Estimate the root of the expression, f (x) = x² – cos x, using: b. False Position Method in the…

A: If the root of a function f(x) lies in the interval [a, b] and f(x) has opposite signs at a and b,…

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

A:

Q: 2. Compute for a real root of 2 cos x- sin Vx 1. 4. accurate to 4 significant figures using…

A:

Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

A:

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: The approximation of the root x* of the function f(x) = -x + sin x - 1 accurate to within 10-³ using…

A:

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

A:

Q: 4. Determine the root of F(x) = 7 sin(x)e--1 using secant method with 3 iterations given X- = 0.5…

A: f(x) = 7sin(x)e-x - 1The iteration for Secant method is given as: xi+1 = xi - f(xi)(xi-1 -…

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: 2. Compute for a real root of 2 cos a – sin Va = + accurate to 4 significant figures using…

A: In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.…

Q: Use Newton's method to solve for x with an initial estimate of x0 = 2n with d* < 0.001. Cosxcoshx =1…

A: (cos(x))(cosh(x))=1f(x)=(cos(x))(cosh(x))-1ddx((cos(x))(cosh(x))-1)=-sin(x)cosh(x)+cos(x)sinh(x)⇒f'(…

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 11 Show that Simpson's rule withn=2 (so there are 2n = 4 subintervals) gives the exact value of (2x…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

A:

Q: 2. Compute for a real root of 2 cos x - sin /x = 4 accurate to 4 significant figures using…

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))