-· EX 2.1 GNen Roint ļ (-2,6,3) dnd ector A =yax + (X+Z) ay O EXPress P and Ā in Cydindrical and SPherical

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: Find order and degree of y'+ (y")? =(x+y")? O a. 2,1 O b. 1,2 О с. 1,1 O d. 2 ,2

A: The given differential equation is                                              y'+(y'')2=(x+y'')2…

Q: _11. What is Sdx? A. +C B. +x + C х-1 C. c. ++ 2x + C x(2x2+3x+6) + C x3 D. _12. In solving S th dx,…

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Q: Evaluate: ftan a sec z 1 sec¹ z dz =

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Q: State whether the following statement is true or false: A vector space may have two or more zero…

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: -2Y dy y°e

A: The given integral is: I=∫y3 e-2y dy

Q: Construct the lagsange, intexpo polynomial AL for the function y=Sin faking the points ス=0 ズ(=ー スー4

A: The given function is, y=sinπx For the given points the functions values are,when x0=1 then…

Q: Calculate 2 4-y2 IL dy de y dx dy. T sinx SSasing dy dx @ $ ydydk

A: Hello, thanks for your question but according to our policy I am answering the first three subparts.…

Q: Identify the type, order, degree, DV, IV and name of the DE. (y'")3+5(y")2-2y' - 5y=0

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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Q: (x – y)(4x + y)dx + x(5x – y)dy = 0.

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Q: السؤال 6 The electro static force given by (ke^2)/r^2, where k=1/ (4nE) 0 صواب İhi

A: False

Q: 7/12 16.r(sec 4.r) dr =?

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Q: d/dx (2x'y²+8x-2y+3)=? Select one: a. xºy2 b. 14x°y? O c. 14x®y²+8 С. d. 14x°y²+2y O e. 2x'y?+8x-2y

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Q: 10 · S (sech u + tanh u)² du

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Q: integral g gren he obteun the basticular PDE (D-pp'- 20, z = 2 x+2y-) Smay - celxy

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Q: Fnd llull, lv , Uov, and d (4,v). (-1,7) , v- (1,9)

A: According to our company guidelines we are supposed to answer only first 3 sub parts. So here I'm…

Q: V24x'y³ • J50x² y° V40m²n • V50m n V28.x*y" 7xy 4 V42 75.xy* V3x 5. 3. 4.

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Q: 13, Use numbers N9N . Which is the reciprocal of 17 b. Which is the recprocal of C Reasoning What do…

A: Given,  The numbers ÷713, 167, ÷167, 713  We have to solve for part a, b  and c

Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: Consider 2a – 3y² = 8

A: Differentiate wrt x

Q: Am + bm = S2m = ame™™ + bme¯ L V' 2| dy sin シ (v-) =[V +(-1)"(v' – v)]. тлу L am

A: Here m≠0.

Q: Z eXZ 4. xyz dydx dz

A: Solution:

Q: Q3) Find dy/dx if 1- y= In /x 2- y3xsin

A: 1) d(ln(x))dxApply the chain rule: 12ln(x)d(ln(x))dx

Q: 29. y' = x² + y².

A: The differential equation has been defined by.Let  Note that the function  is positive and…

Q: Find the constant values of m and n if 2y = 2nx² + 2mx given that when x = 1, y _0 and = 14. dx

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Q: - If y = u – 4u and u = = 3x + r, then dy с. dr 1 dy а. dx 12x3 + 1 12x3 + 1 3u? 4 dy (3u² – 4)(12r³…

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Q: y"+ y"-4y'- 4y- -3-*-4x-6 =0

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Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)

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Q: 2i Find the eguation of the tangent: lime to tul Cur ve y=4x -x* at the point (l,3).

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Q: dy (y tay) - ITY" دا

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Q: Match column A with column B Evaluate the following: So² Sxx+1 x dy dx 4/3 So' SxX x dy dx Choose.…

A: Solution:GivenTo evaluate the followingFormula:∫xndx=xn+1n+1+C

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.