d) V·(pv) = pV • v + vVp

Q: What is tl

A: Given function is: f(x) = 3 + cos (3x) We have to find the gradient of the function.

Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: 2) Prove that: a) dx' dx- b) F) = dF %3D Ldx dx c) [x,p²]= 2h?d/dx

A: To prove- ddx, d2dx2= 0 The mathematical definition of commutators is, A, B= AB-BA Given, L.H.S.…

Q: The spread of a virus is modeled by V(t) = -t° +t² + 12t, where V(t) is the number of people (in…

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Q: Z'1z Where Cil21 ComflexAumber

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Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

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Q: Fird the inversc trons frm of ; F (5) = sz+ 25

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Q: Show: Cov (X,Y) = E[X(Y – μY)]

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Q: ly manufactur nk for the exp- greed that she

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Q: Find F(s). F(s) = £{t(et + e5t)2}

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Q: 2. J Зу /7—Зу?dy

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Q: Çind in fefinite intregal s .2dx - 2x+1 %3D

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Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: of e dydx

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Q: solve for t

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Q: Pro ve 8さt(.)る %3D (Srh)(らtM ー7 \et: ヒこe

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Q: J) 11"+2 + 122n+1 divided by 133 , Vn E N*

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Q: 2 (4-x² r² dzdydx Q5: Find Si * S,

A: We have,∫02∫04-x2∫x2dzdydx=∫02∫04-x2zx2dydx∫02∫04-x2∫x2dzdydx=∫02∫04-x22-xdydx

Q: By using the substitution u = VT + 2, evaluate 6+ 3 dx. ¤(/I+2)²'

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Q: Find mZG. E 35-/2 F 70/2 mZG %3D Submit

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Q: dz IV100-49(In z)?

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Q: 7) sinh 2xdx 8) fcosh vdv 9) f cot ydy pai4 sec? Jwdw

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Q: Wi- Find the where (221) م 270 ل 24 4 2 0 :C للنووزه value of - COSTI Z dz

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Q: *Pivd the general Seltion to the

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Q: tan st dt \+9t?

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

Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

Q: f(x, d,Z)cbxcly dz

A:

Q: im(z,v) →(0,0) F(x, y).

A:

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: d) Sinh'u – Sinh'v = Cosh’u – Cosh’'v

A: According to guidelines we should have been able to solve only one question at a time #d Prove

Q: a) fx² sec2

A:

Q: Find Sea)ax Jf(x)dx if = 56 foR X<to (x fok xZ6 flx): %3D

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Q: What is the approximate value of V16 - V10?

A: The approximate value of 16 -10  is  =4 x 4 - 10=4-10 9 is 3 and 16 is 4 so value of 10 is slightly…

Q: What is the relationship between ZW and ZX? 3,

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Q: 1. b. X %3D in

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Q: 72 Y : 1 Vt2 +t+1 dt ||

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Q: Solve for t in B=Numerator x+y over the denominator t+z

A: The given equation is,

Q: Using appropriate substitution 1 dx V9x² – 36x + 37 Is equal to

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Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: 2 DiFferentiate JE F(E) = Sépsx swx + Jbx SK Sinxt XHI と

A: Differentiate Ft=∫t2tcosxsinx+1x+1dx

Q: Q2 by using Simpsons Rule method to find ,n=6 5 1 dx х 2

A: use sub interval for finding the integral.

Q: dt 4е-t — et

A: ∫14e-t-etdt=∫14et-etdt=∫et4-e2tdtlet  et=uthen∫et4-e2tdt=∫14-u2du

Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: f'«) ių faa) = arcsin Ve^

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Q: te² i· k) dt V1 – ? 40.

A: Solving by definite integral we have

Q: for power substitution method, next step is For S dx xp: 4u³dx 4u³dx 1+ u* 1+ (u*)ã Option 1 Option…

A: Find your answer below

Q: Sx√x + 1dx

A:

Q: f(L,K) + x [loo-PeL-Pak] max dQ

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Q: 222 d. Evaluate dx Vt²-t dt

A: We have to solve this

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.