QUESTION 13 If y = sin?t+ tant, x=-1 – In(- cost) – e* - esinr, find the value of y' when t= 2+ Vze V? 3/7 2/3 6/7 2-Vze ? 6

Q: Siven cos x E and π x<. 5 ", find tan(2x) %3D

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Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: Use Simpson's rule with n = 6 to approximate cos(x) d.x Keep at least 2 decimal places accuracy in…

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Q: 2. For the function y = 3 sin (x + 45°) -2 state the following for 0° < x < 360°. Amplitude: Period:…

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Q: Suppose y = sina, which is TRUE about y? 1 Oy= sin O none of the above y 0 *= arcsing O * = sin y

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Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: Question 10 Using the method of Variation of Parameters, the particular solution Y, for the NHLDE…

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Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: 1 - If xy + sin(e) + arcsin Va dy sin 1 + 1 then what is the value of dz at (, 0) || a) b) 4 8 c)-…

A: Here we have to find the derivative of each term with respect to x and then we have to bring all…

Q: Question 3 Use the trapezoidal rule with n = 5 to approximate %3D 2 cos(x) dx. Keep at least two…

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

Q: i) Find sin 6x+ cos 4x dx. 3 ii) Evaluate || et -dx . Hence, solve 2e* dx . (* +2)" +2

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Q: 1 lim is equal to: (t – 1)2 '

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Q: */10 S sin(10z) arctan(sin 5x)dr = ? a)10(7 – 2) - 2 b)- 5 ) 5 (т — 2) T - 2 d)- 10 Ол - 10

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Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: QUESTION 1 (a) Given y=cosh (x-3). Based on the given function show that d'y d'y 4 sinh (2x) ) dx''…

A: Given that, y=cosh2x-3 To prove, 14sinh2xd3ydx3+d2ydx2-tanhx-3dydx=2y+1  But i think it should be,…

Q: (cos 0 -sin 0) d0 7. J sin 0 8. J (1 – tan 0)² de. 9. sec2 0 tan² 0 d0.

A: 7. Given integral, ∫cos θ-sin θsin θdθ

Q: Question 8 If we have to check the DE Sin(x) +y cos(x) =1 for Exact then M,--- dx -cos(x) sin(x)…

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Q: Where does the periodic function f(x) = 2esin (x/2) take on its extreme values and what are these…

A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the…

Q: COSX 1+Sinx 1+ SinX CoSX (2) See (mx) tan(inx) e a-be

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Q: If cos x is replaced by 1 - (x2/2) and |x |&lt;0.5, what estimate can be made of the error? Does 1 -…

A: We’ll answer the second question first. Notice the question have used first two digits of Maclaurin…

Q: 1. S sina de cos²x

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Q: 3. KIN 2 13² cos x V1+sin x dx

A: The given integral, ∫0π2cos x1+sinxdx

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Given, ∫(1+tan2θ)dθ  The antiderivative of sec2kx is 1ktankx+C The antiderivative of K f(x) is K…

Q: cos? (x) 5 x²e* 6 V1 – x³ 4 - ex 7 sinh(x) 8 x² arctan(x) 9 1- X

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Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

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Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: laploce ď ļ cos' at} 2

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Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: 2 2. cos² ydy 1+sin y

A: The given integration is: I=∫cos2y1+sinydy   We know the common integral. ∫sinxdx=-cosx+C

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

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Q: π/2 sin (cos() sin() dx (Consider initially the first 2 terms)

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Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: Use Simpson's rule with n = 6 to approximate cos(a) dx Keep at least 2 decimal places accuracy in…

A: The solution is given below in the next step:

Q: cosh(2æ) – 1 Verify the identity sinh? (x) using the definitions of the hyperbolic functions.

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Q: In=5 dx Sin^ (x) ( ategrate by parts for findu the Yreduction form (11) by using (i) find In and…

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Q: 39. cos (T + x) 40. sin (2m- xr) 學一) 37T 42. cos 41. sin -

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Q: What is the formula for integrating sin 46 cos 20d0 ? (sin 60 + sin 20) do O S(cos 60 – cos 20) do -…

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Q: /² sin ( cos() sin() dx (Consider initially the first 2 terms)

A: To evaluate the value of given integral. Use the identities: 1.sin A cos B=12sin(A+B)+sin (A-B)2.sin…

Q: tan y = In 2 + e"

A: Given : tany = ln2x2+e-xy

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

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Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

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Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ll solutions of the equation in the interva tan(x + T) + 2 sin(x + t) = 0

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