#5 ở V - (2xy sinz) - (3y~); + (5x> y? z?)k .* and vx ů. ealeulate

Q: m. n. Sex: [ tan³ x dx ex sec³ ex dx

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

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: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: dz 22. Evaluate the definite integral Hint: Trigonometric Substitution 2zv9z2-4 0.

A: To evaluate: I=∫03dz2z9z2-4...(1)

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: Find dydx? for f(x, y) = eXy

A:

Q: evaluate  0∫π 0∫1 1/6∫1/2 xy sin z dxdydz

A:

Q: Jz{sinh³ 4z*)'^ ² - dz 1/4 cosh³ 4z'

A:

Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

A:

Q: Show that (i) | te 3 sint dt 50 -3t %3D

A:

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

A:

Q: y'' + 3y' + 2y = sin ex

A:

Q: I = f, (sinhz + 1)dz. %3D

A:

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

A:

Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

A: We are given a linear second order nonhomogeneous differential equation with constant coefficients…

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

A:

Q: Use implicit clifteren tra fion to find * for the fol llving x*y+ 3xy-x = 3

A: The given equation is x2y+3xy3-x=3 To find: dydx

Q: vE zy sin{z° + y)dzdy Find

A:

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 3. Stanh3x dx = Jsinh3x, Ssinh3x_ dx %3D u = cosh3x du = %3D

A:

Q: Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

A:

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

A:

Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: Test for homogeneity

A: