If x"y" = (x+y)** m+n m. X' d'y prove that = 0 dx?

Q: Suppose dy/dx = x- y and y = 2 when x = 1. Use Euler's Method with increments of Ax = -0.1 to %3D…

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Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: Evaluate double integral.

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Q: ,3 Evaluate the iterated integral dx dy

A: We have to evaluate the iterated integral ∫12∫yy3dx dy.

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: Particular integral of dy +3 dx dy + 2y = e-2a + sin is dx?

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Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: In(5x +3) dy at x = 0. dx (a) If y = then find et

A: Given; y = ln(5x+3)/e5x

Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: dy dr

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

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Q: show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

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Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: Use the Euler method with dx = 0.2 to estimate y(1) if y' = y and y(0) = 1. What is the exact value…

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Q: Find values of p for which integral diverges. dx x(In x)"

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Q: S tan ax secex dx 3

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Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

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Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Compute the differential dy for y = 4x³ + 2x?. dy =0

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Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: In (6x) to x if y = sin (5e') dt.

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Q: Find d when y = 3 In(In(In(x))) dy dx

A: Here we can find the derivative as below

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

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Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…

A: lnx2+y2=secyx

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Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.