Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x) sinh(y) = e* - e +e %3D - 20* -) 1/4

Q: ELIMINATION OF ARBITRARY CONSTANTS

A: The given solution curve is y=C1excosx+C2exsinx=ex C1cosx+C2sinx. That means, the roots of auxiliary…

Q: What best describes the differential equation =-3ty+ cos(t)? It is separable and linear. It is…

A: It is linear.

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

A:

Q: sinh(0)

A: sinh(x), cosh(x), tanh(x) are usually referred to as hyperbolic functions becaue they bear…

Q: The numerical value of tanh(ln(3)^0.5)

A:

Q: solve Partial Differential Equation (Choose one only) 1- дхду ey cos x %3D a?u 2- ay? ди ди a?u ifx…

A:

Q: 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 cosh(x) cosh(x) + cosh(x) – He* + e*) + e* - o*) e* + e*) - e*…

A: The objective of the question is prove the given identi

Q: cos x dx sin x-3sin r+2 1-

A:

Q: S (sin'x-sinx-x' sin* x+x²sin x) dx ? :-x° sin* x + x² sin x) dx ? What is the value of the…

A:

Q: Form a differential equation from the given functions below a) y = Ax + x³ b) y = 5sin(x) + A cos(x)

A: (a) Given : y = Ax+x3 (b) Given : y = 5sin(x) + A cos(x)

Q: 2² cos(4x) dæ

A: The given integral is ∫0πx2cos(4x)dx Using successive integration by parts by taking x2 as a first…

Q: Prove the identities sinh (x + y) = sinh x cosh y + cosh x sinh y, cosh (x + y) = cosh x cosh y +…

A:

Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: 5. 3 :) dx 'tan x cos x

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 5.5.20 – Setup & Solve Use a change of variables to evaluate the following indefinite integral. dx

A: Evaluate by Using of change of variables in the definite integral, ∫x+292xdx

Q: 30. A differential equation Show that both of the following condi- tions are satisfied by y = sin x…

A: The given expression is

Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

A:

Q: tan ydy (1+ln(cosy))3/2

A:

Q: (z-2)(z-2) lim log1/3 sin((2z+ 1)(z-2)). Z→+2

A:

Q: INTEGRAL OF e^(ln tan^2(x)) ln e^(cos(x)) dx

A:

Q: Che number ofunits in Z31[x] is

A:

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

A:

Q: 14. ſ e sin40 cos40d0

A: (14). To integrate: ∫esin4θcos4θdθ Substitute  t=sin4θ t=sin4θdtdθ=4cos4θdt4=cos4θdθ Substituting…

Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

A:

Q: 6. a. Evaluate the improper integral or show that it diverges: x·ln x dx. Show a complete solution.…

A:

Q: 1+sin x 7. y = in+sin x+ cos.x 8. y = In(In x) 9. sin y = In(x + y) 10. y = log(x sin x) %3D %3D

A:

Q: integral e -x cos 2x dx

A:

Q: 1. Approximate sinh(0.6) using the third degree Maclaurin polynomial of sinh r.

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: sin x Evaluate: / dx (cos x) 3 1. tan x- sin x + c an'x + C X, sin'x + C X. 3. 2 4. log (cos2x) +c…

A:

Q: (1+x|) sin²(x)+ sin(x) 1+x| The integral dx is equal to 2

A: Given integral is ∫-π2π21+|x|sin2(x)+sin(x)1+|x|dx

Q: (1-cos 6x)dx Perform the integration:S 1+cos 6x tanx - x +C c. tan3x – x+C A. -tanx – x+C D. tan3x –…

A: We have to choose correct option

Q: tanh x dx O sech?x +c O sinh x +1n(x)+c ]In(cosh x) +C

A:

Q: 1+iz : If w = Find the im age of z|<1. 1-iz

A: Let the transformation be f(z)=w, in which x-y plane is converted into u-v plane.  Where z=x+iy and…

Q: Maclaurine’s series of ∫((cos^2(x) dx)

A: To find → Maclaurine's series of ∫ cos2 x dxSolution →                       ∫ cos2x dx = ∫ 1+cos…

Q: -0.2 e2x sin(x) dx

A:

Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

A:

Q: y = cos(x In 3) log3 (sin x) is: y 3D cot(x) cos(x In 3) – sin(x In 3) In(sin x) y' cos (x In 3) -…

A: As we know that; The Chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f·g'   And ddxlogax=1xlna…

Q: Use integration by parts to derive a reduction formula for x"e dx. Use the result from part 1 to…

A:

Q: integral (x-1)sin pie x dx

A:

Q: cos x sin xdx COS

A:

Q: sin x+1 Soru 4. I = -dx integralini hesaplayınız. (20Puan) cos x+1

A:

Q: Two methodsa. Evaluate ∫x ln x2 dx using the substitution u = x2 and evaluating ∫ln u du.b. Evaluate…

A: ∫xlnx2 dx a. Put, u=x2⇒dudx=2x⇒du=2x dx⇒du2=x dx Therefore, ∫xlnx2 dx=∫lnu du2=12∫lnu du=12∫lnu·1…

Q: Find Sn{sinh(x)} = %3D O A. Lnn(-1)" sinh(L) L2+n2n2 O B. None O C. Lnt(1-(-1)" cosh(L)) L² +n²n² O…

A:

Q: sinh (e-*) dx e* cosh(e¯*)

A: Given,∫sinhe-xexcoshe-xdx

Q: cosh 3 хр. 15) 1-sinh 3

A: Solution

Q: sin 0 d) lime tan 0 sin z-cos z + 1 e) lim, 0 3z

A:

Q: Evaluate using Integration by Parts. cos(13x) dx (Express numbers in exact form. Use symbolic…

A: