Select the expression that is equal to cosh²(n x)–1 cosh'In x) O x?-2x+1 x2 +2x+1 O x? -1 x2 +1 2 1- e* + e*

Q: Find the sum from n=1 to infinity (sin(6/n)-sin(6/n+1))

A:

Q: Determine a two term expansion for the large roots of x = tan x and rtan x = 1.

A: "According to the guidelines we will solve first question. Kindly repost second question…

Q: The smallest positive, nonzero root of cosh x cos x - 1 = 0 lies in the interval (4, 5). Compute…

A:

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: Find the integral of ∫tan^5(4x)dx

A: Given Data: Integrand: ∫tan54xdx   let u=4x   The derivative of the above equation is, dudx=41dx=du4

Q: 5) Integrate 2x cos (x²-5) with respect to x.

A:

Q: 1- , S" cos(x)esin(x)-8y dydx

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

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: Verify that the equation is an identity. 2T X+ COS 3 TO + sin +X =0 6. Apply sum identities to each…

A:

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

A: The False position method is a technique used to find the approximation of the root of the equation…

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: Let In = fcos" rdx. Show that: 1 In n n-1 COS x sin x + n-1 -¹ n -In-2, n ≥ 2.

A:

Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: 3. sin(3x) = 3s in x – 4sin³ x

A:

Q: Use residue to evaluate the integral 3+ 2 cos 0 do 5 + 4 cos 0 0.

A: Given integral is, Let C denote the unit circle |z|=1. So,

Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

A:

Q: Find the first four nonzero terms in a 6y"-(cos x)y'-y = 0; y y(x) = +... (Type an expression that…

A:

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

A:

Q: Use false position method to find the root of f(x) = e* (3.2 sin x - 0.5 cos x) on the interval…

A: We need to find the root of fx=e-x3.2 sin x-0.5 cos x The given interval is 3,4 Also, we are…

Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: */16 etan(1r) sec2(4x) dr

A:

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: Find the indefinite integral. [ cos 3xar sin33- sin 3r +C 6. O sna(3- sn'ax) sin3 3-sn 3 +C sn3x…

A:

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

A:

Q: (2x³ + 5x-4) dx

A: Solved below.

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

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

A:

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: 2. Show that by using MEAN VALUE THEOREM 4-n < tan-1 v – tan-1 u < 1+v2 if 0< u<v 1+v2 3 <tan 25 -14…

A:

Q: Assuming that |a| < 1, find the value of cosh ax dr. cosh x

A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

A:

Q: sin 3xdx Evaluate: S 4+cos?3x

A:

Q: Prove the identity.   cosh(x+y) = cosh x cosh y +cosh x cosh y

A: Given information: coshx We know that, coshx=ex+e-x2sinhx=ex-e-x2

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

A:

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: dN + N = Ntet+2 dt

A: we have to solve first order of differential equation given below

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: Use residue to evaluate the integral 2л 3 + 2 cos 0 do 5 + 4 cos 0

A:

Q: Prove that : 1. Sinhx= In(x+x² +1)

A:

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…

Q: Approximate all solutions to 8-cos(x)² – 6·cos(x)+1 in the interval [0°,360°) x = V degrees Round…

A:

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

A:

Q: How many integers are there in the domain of the function f(x) = ln (x² – x – 12) + v25 – x² +…

A: The domain of a function is the set of input or argument values for which the function is real and…