4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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Q: Find z in 2= Sinh (4-j5). cos (4-5) express in polar porm

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Q: What is the antiderivative of g(x) = 2 cos(x) that contains the point (7, 0)? 4 O 2 sin(x) –V2 O 2…

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Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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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 xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

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

A: This integral can be solved by changing the order of the integral. The order can be changed by…

Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: (Find the integral curve of the following equation passing through the given point). y = 4 cos(x),…

A: Given dy/dx and point we have to find equation from this

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: Evaluate the integral cos"() sin(x) dæ cos'4 using the substitution u = 1 = cos(x). | cos"(x) sin(x)…

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Q: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…

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Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: Q1\ Differentiate the following (c 1)2xsin-13x 2)y = In *+1 Vx-2 %3D 3)y %3D sin-1 2x

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Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

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Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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

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Q: 4 sin (In t) cos`(1nt) dt 5.

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu