dx 1 In х —а (x – a)(x – b) a - а — b х — Ь +C where a, b are constants such that a + b.

Q: Let y=5√xFind the change in y, Δy when x=1 and Δx=0.4Find the differential dy when x=1 and dx=0.4

A: Given: y = 5xTo find: 1. ∆y at x= 1 & ∆x =0.42. dy  at x = 1 & dx=…

Q: Let y 3x?. Find the change in y, Ay when x = 2 and Ax = 0.4 Find the differential dy when x 2 and dx…

A:

Q: Let y = V7- x. Find the differential dy when a = 4 and dx 0.3 -0.0866 %3D %3D Find the differential…

A:

Q: Let y = 5a2. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4…

A: ∆y = 5(x + ∆x)^2 - 5x^2= 5(x^2 + 2x∆x + ∆x^2) - 5x^2= 5(2x∆x + ∆x^2)= 10x∆x + 5∆x^2 So when x = 4…

Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

A:

Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ar 0.4 Find the differential dy when a = 2 and…

A:

Q: Let y 5æ?. %3D 0.1 %3D Find the change in y, Ay when x 5 and Ax 0.1 Find the differential dy when x…

A:

Q: a- If w = x² + 2xy and x, y change from initial values (x = 1, y = 3) By amounts dx = 0.01 and dy =…

A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

A:

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Let y = 2/x. Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3…

A:

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

A:

Q: Exact difterential egation 4. (1+In(xy))dx+ 1+ dy=0 y,

A: Given differential equation is, 1+lnxydx+1+xydy=0   ...................(1) Comparing with Mdx+Ndy=0…

Q: nd ifzxy+In(x) . x-r-I and y=e dt

A:

Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

A:

Q: (ii) o S(2xy + z)dx dy dz z=-1 :0 Jx=1

A:

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: Let y = 5 x. %3D Find the change in y, Ay when a = 5 and Ax = 0.3 %3D Find the differential dy when…

A:

Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

A:

Q: Let y = 4x. Find the change in y, Ay when x = 5 and Ax = 0.3 Find the differential dy when x = 5 and…

A:

Q: Let y 52?. Find the change in y, Ay when r = 5 and Ar 0.1 Find the differential dy when x 5 and dx =…

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Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

A:

Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: Approximate V 34 using differentials. A 2.023400 B 2.024397 c) 2.025000 D 1.975000

A: Given (34)^(1/5)

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

A:

Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: 2 y +-y=D = 2t³ In(t), t> 0. (a) Verify that y = t*(1 – 2 ln(t)) is a solution of (1)

A: Take y, differentiate and substitute everything in equation (1).

Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: dy Given y x" In (2x), determine dx ax"- In (2x) + a-1 a.a"- In (2x) + 2.x O...n 1 None of these ax…

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Q: Q.1. Use the differential dy to approximate ay when y=3x-2 and x changes from 2 to 2.03

A:

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and dæ = 0.4

A:

Q: df Q4) A) Find dx by using chain rule if f = , u=-1 , x=-1 u+1 B) Evaluate the following integral:…

A: A) To find the derivative of the given function f=u-1u+12 with u=1x2-1

Q: Approximate V 34 using differentials. A) 2.024397 1.975000 B) C) c) 2.023400 D) 2.025000

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Q: Q2: Sdve the differential eqpeation d²y =20"t 9Sin 2x -2Cos 2x %3D

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Q: Let y 3T. Find the change in y, Ay when x 2 and Ax 0.3 Find the differential dy when a 2 and da 0.3

A:

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: 26. Let y= Væ. a. Find the differential dy. b. Evaluate dy and Ay if æ = 1 and dx = Ax

A: a) Given that , To find :…

Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: Let y = 3a. Find the change in y, Ay when x = 1 and Ax = 0.4 Find the differential dy when x = 1 and…

A: Given that: y=3x       NOTE: As per our answering guidelines, we can only answer 1 question or 3…

Q: Let y = 4/T. Find the change in y, Ay when x = 4 and Ax = 0.1 Find the differential dy when x = 4…

A: Given:- f(x) =4√x To find :- Change in y , Δ y when x = 4 and  Δ x=0.1  Differential dy when x= 4,…

Q: Let y = 4ĩ. Find the change in y, Ay when x = 4 and Ax = 0.3 Find the differential dy when x = 4 and…

A:

Q: Let y = 2x2. Find the change in y, Ay when x = 1 and Ax = 0.1 Find the differential dy when x = 1…

A: Given function is y=2x2, The change in y at x=1 is given by,…

Q: 8 dz dx dy 4+x2+y² V2 V4-y2 Evaluate S y O z In 2 O In 2 O 2n In 2

A: use polar coordinates and substtution method for solvng such integral

Q: Let y = 2x². Find the change in y, Ay when x = 4 and Ax = 0.2 Find the differential dy when x = 4…

A: It is provided that y=2x2. We need to determine ∆y for x=4, ∆x=0.2 and We need to determine dy for…

Q: Let y = 3a?. Find the change in y, Ay when x = 1 and Ax = 0.3 Find the differential dy when x = 1…

A:

Q: Let y = 3x². Find the change in y, Ay when x = 1 and Ax 0.1 Find the differential dy when x = = 1…

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

Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.