1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

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…

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Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

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Q: 1.4 Calculate an approximate value of the integral S (sinx – Inx + e*) dx by - 0.2 dividing the…

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Q: 1. Jo cos x sinh x dx

A: Explanation and solution is given below....

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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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: 14. Find the antiderivative of 5sinx In 5 cosx. a. 5cosx +3 c. 5sin x In b. 5sinx-2 d. 5 sin x + 7…

A: Anti derivative of the function

Q: 4. sin 'xcos 2 O J sin xcos"xdx (8)

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

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: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

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Q: 1.4 1. Calculate an approximate value of the integral So5 (sinx – Inx + e*) dx by dividing the…

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Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: 2) Find L{te"sin5t} using two methods. ans: (s+2)2+25

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Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 1/2 2. Approximate the integral: 1 - cos(2x) dx within an error of 0.01. x2

A: According to question given that∫0121-cos2xx2dx within an error of 0.01

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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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: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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

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Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: 5) S V2 + sin 3t · cos 3t dt

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Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

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

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Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

A: Solution I=∫sinin x dx        Let  lnx=t⇒x=et         1x dx=dt          dx=xdt…

Q: I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6.…

A: Topic - Derivative of a function Power rule: ddxxn=nxn-1ddxln(x)=1x

Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: Please I want solution of question 8 with step by step. Many Thanks

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

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Q: In( cosh(3x)+sinh(3x) )= Select one: O 3 sinh(3 x )+ 3 cosh(3 x) O- 3x 01 zero None O 3x

A: Formula to be used sinh x = [ex– e-x]2cosh x = [ex+ e-x]2

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: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

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: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: ons z = sin y arn

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Q: 49. * ccunlı * sinh xdr = In 2 e€u«lı * sinh xdx = A. e - e B. c - c C. ei - e В. D. ci - 1

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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: 1%1… l.令 > OX 101:00 i learn.ejust.org/current, :D tan-(x) dx = %3D V3 n - In (8) - In (2) V3 None…

A: Since you have asked multiple question, As per our guidelines, we will only solve first question.…

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: dy.xandy in =cos = COS e

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Q: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: 10 - S sin(8a) arctan(sin 4x)da integralinin değeri aşağıdakilerden hangisidir? 9118002 8(T – 2) a)…

A: Given that  The integral  To evaluate the integral

Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.