y y = flx) 4+ (0, 2) 3+ (-2,2) 1- (2, 2) -5-4-3-2-1 1 2 3 4 5 -2- -3- -4- + en d

Q: f (x, y) = 3x²: f (x, y) = x² + 3y²: f (x, y) = y – 2x?: f (x, y) = 5x² – 5y²:

A: The function f(x,y)=3x2  Level curves are made by fixing values of fx,y=k.…

Q: y" +6y' + 4y = 10e ; y(0) = 0, y'(0) = -2 Answer: y = et -e-t +e-* 3

A: We are given the differential equation : y''+6y'+4y=10et Taking Laplace transform both sides, we…

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

A:

Q: (2siny + 1) = 4 and y(0) = what is x when y =n?

A:

Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: 6. x = (y/6) + 1/(2y) from y = 2 to y = 3 %3D

A:

Q: f (x, y) = 169 x² + y² at (-3,2).

A:

Q: Find y dy S using the substitution +5=√√y+2 √y+2 (√3+2-5) (5√y+2+y+21) +C 3 (√x+2-5) (5√3+2-y+24) +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: The given equation is z=y3-24-2y3 The objective is to find dzdy. The product rule for derivates is…

Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

A:

Q: y''+3y=6x; y(0)+y'(0)=0; y(1)=0

A:

Q: y"(t) – 4y'(t) + 4y(t) = 4e2t; y(0) = 1, y'(0) = -4

A: Given differential equation y''t−4y't+4yt=4e2t and y0=1, y'0=−4. Take Laplace transform both sides…

Q: 3) ryy'-r. +1 = ry +y +r+1. Ans.: y +1 x(Ce-1).

A:

Q: 5 y"+y'+y =t-Un/2(t) 4 y(0) = 0, y'(0) = 0 2

A: Consider the given differential equation.

Q: 9. T: R² → R², T(x, y) = (x + 2y, y – x) 10 T. D2

A:

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: Q.2 JJR ex2-2 dxdy, where R between x2 =-y, y = 0 and x = -3 , y = -9

A:

Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: 5) /x + y + y² + x² = 18, y'at (0,4 )

A:

Q: f(x, y) = x* + 2y³, R = [1, 2] × [2, 3]

A:

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = -3x2y3 + x3y

A: Given that, fx,y=-3x2y3+x3y Then we get,…

Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: y" +2y'+ y = t O y = t-2 O y= 1/2 (t) O y = t O y = 2t -1

A:

Q: Se xye" dy, C. x- , y-, z- , 0 <te1

A:

Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

A:

Q: 3x²y if (x, y) = (0, 0) + y? if (x, y) = (0, 0) f(x, y) = { x +

A: In this question, we have to check the continuity of a function of two variables.

Q: or the DE y' = xy2, y(0) = -1. Then, y(2)=

A:

Q: 24 y 3D y = 10. 11. V1O 45° 30 y. y y = - y = 14. 13. y 45° 30° X = 17 y = z =

A:

Q: xy = 9, y"' at x = 1, y = 9

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative

Q: Find y dy ·S using the substitution u +5=√√y+2 y+2 © ²(√√y+2-5) (5√/y+2+y+24) + C…

A:

Q: (c) y" - ry +y = ', y(1) 1, g/(1) = -1, r>0

A:

Q: 2. x'y-x'y 12 at (-1,2)

A:

Q: 3. x = (y/3) + 1/(4y) from y = 1 to y = 3

A:

Q: y" +2y' + y = t O y = t-2 O y = 1/2 (t) y = t O y = 2t -1

A: To find the particular solution to the given differential equation first write it into operator…

Q: (b.) ry' + y = 1 In(r), with y(1) = 0

A:

Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

A:

Q: p = 2x + 4y + 6z x + 2y > 200 3y + 4z 0, y > 0, z 2 0

A:

Q: roblem. y" – 2y' + 2y = e-; y(0) = 0, y'(0) = 4 %3D

A:

Q: - find x, y z Select one: а. X-3,у-2,z-1 b. x=3,y=-2,z=1 С. X-3,y-2,z-1 d. x=3,y=2,z=-1

A:

Q: C(-1, 3) and D(-5, 7) Vex, - x,} +(y, -y.: d%3= X, = _ ; X, = iY2=_ Y=

A:

Q: 5. y" + 3y" – 4y = 40t²H(t-2); y(0) = 0, y'(0) = 0, y"(0) = 0, y''(0) = 0 %3D

A:

Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

A:

Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.