4. lim メ→3 メ-3 5. lim メーラ X-1

Q: Зх +8 (y-3x) dydx y + 5x —1 ) — 5х (y – 3x)"

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Q: 3) 2y"+y'-y = x + 1

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Q: 5 y = 2 – x 6 y = -5x 7 y = 2x' – 3 8 y= x + 8 9 y= 10 y = x 11 y = Vx +1 12 y = 4 + 3x 2.

A: Remark: A function g is said to be inverse function of f if  f(g(x)) = x for all x in the domain of…

Q: should i write it with variables like x = 11, y = 11, z = 4? but it says exact number, no tolerance.…

A: The answer has exact form. You will not have to enter the variables.

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: 2. y" – 2y' + 10y = 10e2x ; y(0) = 0; y'(0) = 1

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Q: (4) y" - 3ry + Ay = 0; y(1) = 2. /(1) =1

A: Given that (4) x2y''-3xy'+4y=0,  y1=2 and y'1=1 The given equation is a homogeneous linear…

Q: 2 y+ 3 dy y + 5y + 6

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Q: 2 lim y² - 7y + 12 3 y → 4 y - 64 1 48.

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Q: 5. y" + 3y" + 4y' + 12y = 8cos2x – 16sin2x

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Q: Differentiate: 1. y = x*-x + 5 2 2. α : e+1

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Q: 1. y = Vz + 3z – 1

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Q: ve for y esec(4y²-6y+14) = 3x + 1

A: We have to solve for y of the given equation

Q: Y.マy+12Y-2é, y)=3.5 ,y--lo 3も %3D

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Q: 1 (y– 5)³ dy 9. y3

A: we use substitution method to solve this integration

Q: y"=4y'+3y=20cosx

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

Q: 4y " +4y'+ y = 0; y(0) = 1; y'(0) = 2| %3D

A: In this question, we solve the differential equation (IVP) and answer the given four points. the…

Q: ý +4ý + 3y Y6) = y'(0) = 1 %3D to

A: Given that

Q: 7) y"+4y+20y-23sint-15cost y(0)-0, y'(0)--1

A: We have to solve given problem:

Q: 4– 3y? – y3 5. lim y--2 6 – y – 2y²

A: To evaluate the limit: limy→-24-3y2-y36-y-2y2 Solution: It is 00 form which is undefined form. When…

Q: Solve the linear system

A: the given system of linear equations is: x+y-2z=4x+3y-z=72x+y-5z=7 we have to solve the given system…

Q: 2. = dy (-5x + y)² – 4

A: We need to solve the differential equation by substitution.

Q: y ce + 3r O y'+6y 2t (t+ 1) O y'+2y = / (1+ 6) 3. y'-2y 61 (t- 1) O y'+ 2y = 61 (1 + 1)

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Q: 4) y – 4y = 8u(t – 3), y(0) = 2;

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Q: 20+y dy 20-y -20

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Q: Solve please

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Q: 23- y" + xy = 0, y' (0) = 0, y' (L) = 0

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Q: 3y +5 (5y-7)2 dy

A: We can find the integration as below.

Q: limy 2y³ + 5y² -7 00 10y³ – 9y+12

A: limy→∞2y3+5y2-710y3-9y+12

Q: ), y(0) = 4.6, y'(0) = - %3D

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Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: now 1. yA y = 5x-x² 2. (4, 4) y =x

A: Hi there! Thank you for the question, but as per our guidelines we can solve only one question at a…

Q: X + y + z = 11 X - y + 5z = 17 5x + 5y + 5z = 19

A: See the details solution in below

Q: [a] -(-x)= x [b] (-x)y = -(xy) and (-xX- y)= xy

A: We use The fact that (-x)+x=0 and x*0=0

Q: π 9- y² dy y 2 π 6.

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Q: 1. y+ /x + y = 2x at ( 2, 2)

A: Follow the procedure given below.

Q: 1) y" – 10y' + 25y = 8e- y(0) = 1, y'(0) = -4;

A: Follow the steps.

Q: 4t^2y"+8 ty'+y=0, y(1)=-1 and y'(1)= 3

A: We have to solve the following Cauchy Euler differential equation: 4t2y''+8ty'+y=0. The initial…

Q: 4y" + y' + 5у %3D 0 у (0) 3 2 y'(0) = 1 у" (0) — —1 %D

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Q: 2) 2 dy +9 = 0, y(0) =-3

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Q: Differentiate. 5x y = et 5- 5x y' = %3D et

A: Yes above answer is correct, lets see how to solve... This is the simple question based on…

Q: y + 1 xy' + (tx* t2) y. 8e 7 24

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Q: Y"+y'=secxtanx by using variable cofficients

A: It is a second order differential equation with variable coefficient:  y''+y=secxtanx we can solve…

Q: y(IV) – 16y = 0 16у %3D yaV) + 4y" + 4y = 0 6.

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Q: 2. Differentiate the following: (a) y = x²z

A: The given expression is: y=x2x   ...1   As we know the Product rule: f·g'=f'·g+f·g' The Power Law:…

Q: 1 y dy Sza 3 (a²-y²)²

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.