The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے + 15( 2 2 25 + x3 +1 (c) + C 2 (x³ + 2³ + 1)* (d) 10 +C 2 (a* + a* + 1)* 2 x5 + x3 + 1 where, C is an arbitrary constant.

Q: 21. Кх, у) 2х -у ys 4x + 6 5 * 4y s 7 2r + ys7 бу X-6y z 10

A: Step-1 f(x,y) = 2x-y            y ≤ 4x+6 ⇒ 4x-y ≥-6            x+4y ≤ 7           2x+y ≤ 7…

Q: 5) Find the general solution by using reduction of order method to (x² + 1)y" – 2xy' + 2y = 0 given…

A:

Q: 12. Solve using Cramer's Rule: 2x z = 14 3x - y + 5z = 0 (4x + 2y + 3z = -2

A:

Q: .3 2- S(y² – 4y + 2 ) dy

A:

Q: Verica didn't solve this radical equation correctly. Here is their work: U2x-2 = x- I %3D ©…

A: We have to solve the radical equation 2x-2=x-1.

Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

A:

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

A:

Q: Consider the problem maxx [-(x - 4)]² subject to x21. Use Thus the Kuhn-Tucker conditions to find a…

A: We are given the following problem.       maxx -(x-4)2       Subject to x≥1 Let us simplify the…

Q: /4y² - 25 -dy

A:

Q: Maximize B=6xy^2​, where x and y are positive numbers such that x+y^2=4.

A:

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: A Ⓒ Using integration by parts to solve f √4x²+k -2√4x²+k -√4x²+k 2√4x²+k x³ dx √4-x² and letting u…

A: Let's find.

Q: Integraate :S, 22+x+! d>x 2.

A:

Q: 7. dz | zV 36z2 - 25

A:

Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

A:

Q: B. Use Cramer's Rule to find the solution to 2x1 + x2 + x3 = 2x1 – 3x2 – 3x3 = 3 - - -2x1 – 2x2 +…

A:

Q: 2/3 Lal(2x²4). (2x+3 3

A:

Q: per integral test, SELECT ALL AP A) (-1)" B) none of these 8n2 + 3n + 3 (-1)" dz 8z2 + 3z + 3…

A:

Q: /4x+ – 12x² +7 xdx . Evaluate the integral A) -(4x4 – 12r²+7)/2 +c 24 © ! (21--3)/- 121+7 – 2 m…

A:

Q: ALL WORK MUST BE SHOWN 1. What is the product of 5x²z³+ 3xy - y² and 4x² + xyz + 3y?

A: Product one by one we get

Q: Jy > -x² + 6x – 12 ly -x² + 6x – 12 ly>x² - 4x – 1 Sy -x² + 6x – 12 Lyzx? - 4x – 1 Syx² – 4x – 1…

A:

Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x +1)? Select the correct answer below: In (3z2 + 4z + 3)…

A:

Q: If g(x) = f(r²), then g(-3) =

A: We find g'(x) using the chain rule

Q: Ex:- Min Z= X-3 X2-2 X3 %3D sub to 3X1 - X2 + 2 X3<7 -2 X + 4X2 く12 -4Xi+ 3X2+8X3 slo Find anew…

A:

Q: Evaluate ( ax"+5ax*+12ax*+llax²+3ax+10a x4+5z³+14x²+17x+7 dx * + 24. + In |a2 + 3x + 7| - arctan In…

A:

Q: 2n bị 2n 2n paz x a, , b2 = a, xa x a, , bz = a, x -аз ха,,

A:

Q: If y=2x²-4, what is its inverse? or Oy¹--√2 Dy^--, DOIN such that xs-4 such that x2-4 such that x20…

A: Given, y=2x2-4 To find the inverse, we need to swap the variables 'x' &amp; 'y' x=2y2-4 Now solve…

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

A:

Q: find The Six Solutious of The eq- 6 Z+27+2

A:

Q: 2. dy axta¹ x-In√x²t)

A:

Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x + 1)? Select the correct answer below: O In (3z² + 4æ +…

A: Given, rx=lnx3+2x2+3x+1

Q: 14 (3 3 1f y=/xL5x²–36 x15x²-36 X23x²+¥x-12 show that dy dx4 24

A:

Q: Differentiate : a. y= In(2x^2 +4) b. y= In(ax^2)

A: Differentiate (a) y=ln2x2+4 (b) y=lnax2

Q: 2) Find dy of: 7x 5 上 (3-2x

A: We know that  ddx(xn)=nxn-1

Q: Solve using Cramer's Rule only. 4w + 3x – 5y + z = 6w – 5x + 2y+ 2z -9w + 9x + 6y + 3z = 6 3w + x +…

A:

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: 6. Differentiate: y x2 + 3x – 1 x²+1 -(x²+1) В. А. x²+3x-1 (x²+3x-1)2 -x2+1 x2-1 С. (x²+3x-1)2 D.…

A:

Q: 2. § (5z² - 7z + 3) dz from z = 2 to z = 1

A:

Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 6. Find the general solution of (x + 2y - 1) dx + (x +2y +5) dy = 0 х +у - 6 In(7 -х - 2у) 3 x - y +…

A:

Q: 19. (x, 4x), (-2x, 3x), given that x < 0 -XV10 (since x< 0, Vx2 = -x) %3D 20. (x, 4x), (-2x. 3x),…

A:

Q: What is the coefficient of x'y' when (x – 2y)² is expanded using the - Binomial Theorem?

A:

Q: 5) Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A: Use the procedure of reduction of order to solve the given differential equation as in next step.

Q: x - 6x = 2r – 4y Hom: of the funsti

A:

Q: 7. Express as a single traction 1 4 X +1 x - 2 8. Express as a single traction. 2x - 1 + 3x + 1 4 3

A:

Q: Is X4 + 3X2 – 2X +I irreducible in (Z/5Z)[X]?

A: Answer

Q: 6 4 for f(x, y) 3 3x у - 4x'у". 5 3 Verify that дх ду ду дх df 4 5 18y x - 20y°x of 5 3 4. 2 18x°y -…

A:

Q: Prove that equation x^2 + y^3 = 60 does not have any positive integer solution. Prove by…

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.