EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: Find : dw/dk α w=2 sin m ka 2

A: To find dw/dk for the given w

Q: IX. Find y' if 1. (5 pts.) y = 2 In (cos (Tx)) 2. (6 pts.) y = csc² (Arcsec (Va) + e-)

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Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: Question 18 If f(x) = fr30cos(t)dt, then f'(VT) = 37 sin (7) cos (n) B. C 37 COST Зт сos (т)

A: Find the derivative of f(x) using  fundamental theorem of calculus

Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: sec2 t dr 42. dt (п, 4) TT tan t + 1'

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Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: tan 0 d 30. dO sec² y dy

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Q: QUESTION 4 If y = (sinx), show that %3D (1 – 2) dy dy 2. dr? dr

A: Explanation of the answer is as follows

Q: sin(2t + ) dt = 00 64e 4. O O OG

A: Here in this problem we have to find ∫0∞sin(2t+π2)e2t-3dt

Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

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Q: QUESTION 4 dy Find if da 1- cosh a 1+ cosh a

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Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Question 14 d (tanh -'(cosx)) dx A cschx B) -csCx C) -secx D cothx

A:

Q: 2.)S csc-³«(cosa)³da

A: Given ∫csc-3 α (cosα)3dαTo evaluate the integral:

Q: Sect sec't dt Tari'la)

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Q: Question: Y" - 2y' + 2y = 5 Sin T + 10 Cos T, Y (0) = 1, Y' (0) = 2

A: I have provided this answer in step-2.

Q: set E: Problem #6 Find the equation oF the line tangent to at x = 5r FCx) = cos?x -sin? ) %3D

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Q: Question 1.i.) A truncated sine wave { sin5x, -T <x <T y = f(x) = 0, otherwise

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Q: 9. If I = 4 sec22(x) tan36(x) dx = uP (1+u²)ª du , then la a = b p I| || || I|

A: We have to find a, b, c, d

Q: Eliminate the parameter t from the following. Sa(t) = 2 sin t + 5 ly(t) = 5 cost – 6

A: Rewriting the given equations:

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: A particle moves in a straight line with acceleration ?(?) = sin ? + 3 cos ?, initial displacement…

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Q: 9. TC/2 (3 sin² t cos ti+ 3 sint cos² tj + 2 sint cost k)dt

A:

Q: Problem 3. Prove that 2 (b) L(r} : a (a) L{sin at} : %3D s2 +a? (c) L{cosh at} : 52 – a²° -

A: Explanation of the solution is given below...

Q: cos(s) d u du = ds -8

A:

Q: Question 3 Differentiate 5* sec(e*) (A 5* sec (e*) [e*tan (e") – In 5] B 5X In 5 sec (e) [tan (e) +…

A: we have to differentiating  AS per guideline we have to solve one question

Q: Question 6 af Given f = esec (#) -ya+y, find dy (#) sec² (=) ye NO -y+In (y)

A: Given :f=esecxy-yx+y

Q: (d) > sin km/2 S.

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Q: SITUATION 5. Find du/dx for the following: * (€);y = VT+ 1 +x² 37. u = sin-1

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Q: i?? cos(2t) dt csc(10t3)

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Q: Use an appropriate local linear approximation to estimate the value of cos(29°). cos(29°) -

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Q: Question 8 A Ísec xdx= tan z + C A B) csc?z + C cosz +C

A: AB8 Q.8) The given integral is ∫sec2xdx

Q: :S (1 – ±) cos(uw – In w) dw.

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Q: w sin(1ow)dw

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Q: 2. Find sin(72) -dz. where C: z(t) = 2 cost+i (2 sint). Os ts 2m.

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Q: Example : Find S“ (cos ti + sin tj+ tk)dt

A: We can do integration w.r.t. dt

Q: If y = (tane) /28 +1 find dy then choose the correct answer: %3D dx

A:

Q: Which of the following is equal to s v² cos (v³)dv ? A sin 1 8 jsin 1 O Option 1 Option 2 D. sin C.…

A: The solution is Option B 13sin(1)

Q: Question 1.i.) A truncated sine wave { sin5x, y = f(x) = 0, %3D otherwise

A:

Q: Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).

A: w=siner,  r=3sins+π6 Differentiating w=siner with respect to r, we get…

Q: QUESTION 2 If y-sin-¹ z, show that d'y Hence, deduce that -(1)-(2) - <- 0. dz = M dz dz

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Q: If the position of a moving object is s(t)=(sin t)² meters above zero at t

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Q: Problem 1. What is the distance travelled by a point during the time t, if it moves in X- Y plane…

A: Given that x=asinωt and y=a(1-cosωt) are relative to each other. We need to find the distance…

Q: QUESTION 18 2ay" = 17 when =/2. y' "x= Arctant3, y=V1+r6, find the value of a if O -22

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Q: Question 12 of 12 fe #0. dz and ye-8 sin 4z = 4z %3D dz dx dz dy II

A: The objective is to find the partial derivatives.

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: a(t) = sech () tanh ()-ež. I t cle.

A: