S Prove that L(cos 3t) : %3D (s2+9)

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: The DE : y'= e 5x-7y is seperable Select one: O True False

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Q: Find Cマ×F ) マ if F (Miyız) 398 sin ni + COs C 8M - gy) t 10zK

A: Given : Fx,y,z = 8sinxi + cos8x-9yj+10zk

Q: Evaluate fl. 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

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Q: R4 for g(x) = cos(xx) on [0, 1]

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Q: = cos(x + y), when x = 0, y = " %3D

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Q: Use there solue the IVP 2. of xZ dn - 24y cO g (6) = -4 y'Co) = t 4 y Cx) =

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Q: Evaluate cos zV1+ cos². dædy

A: Given double integral is                    T=∫01∫arcsinyπ2 cosx1+cos2x dxdy ⋯⋯⋯⋯⋯⋯ (1)

Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

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Q: O Verify that you (-00, os). Cos (zt) is a salution to y"- Sy= -9cos(2€) on

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Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: calculate L4 for f(x)=76 cos(x/2) over [2pi/4, 2pi/2]

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Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

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Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: 3. Show that the following ODE is homogeneous then solve it. 2xyy' = x2 + y?

A: 3). Given: 2xyy'=x2+y2 So, we can also write as: 2xydydx=x2+y2dydx=x2+y22xy....1 Let,…

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: 2. Let R(t) = } sin 4t î – bcos“(21) j + 2t k. E

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Q: Fird the Aren of the Reyion c2-9 cos In teriur of (2€)

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Q: O prove that : (2) DO 2x e dx a e +b where a, b >o

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Q: :Find the Value af the integral COs Z d2 2(Z-7) 121=1 2. 22+1 COS Z JZ 3. 121=1 z (2-3)

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

Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

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Q: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

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Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: Evaluate fo (6+3 cos a) da using Trapezoidal Rule (n=2). O 12.43167 O 12.26896 11.78097 O 12.386125

A: The given problem is to find the approximate value of the given integral using Trapezoidal rule with…

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: Q2// I= f, (x² cosx) use Simpson's 1/3 rules, with n=4.

A: We have to find the integral using Simpson's 1/3rd rule. In first question there is not equal…

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: show that1) d/dz [cosz] = -sin z

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Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Q3) for f(t) = sec-(6t- 1) and g(t) = tan (6t - 1) show that s'() = g'(t). %3D

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Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: 1. In each of the ff., find frz; fy, fry, fyx- 2x2 2. f(x,y) = tan

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Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: Is this correct?

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Q: The ODE dy (z+y+5) is separable. %3D dx Select one: O True CO False

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