Draw a picture that shows the difference between dy and ∆y.

Q: Given the double intergral 3 S.³ To √²+y² Evaluate the above dy dx intergral using cartesian…

A: some of the formula of integration . ∫1x2+a2dx=ln|x+x2+a2|+C∫xndx=xn+1n+1+C

Q: Evaluate L e* dx dy by using trapezoidal and Simpson's rules.

A: Given that, ∫02∫01ex+ydxdy By trapezoidal rule, ∫abf(x)dx≈h2f(a)+2fa+b2+f(b) where h=b-an…

Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: Given x = 2 In(t) and y= 4 t then find dy dx dy da?

A: Given, x = 2 ln t  &   y =  4t2

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: E e dt Evaluale

A: Gamma function

Q: Evaluate e Cos I dx with tolerance e = 0.05 using the Composite Trapezium Rule. %3D

A: Equation is f(x)=ecos(x).The value of the table for x and y x 0 0.25 0.5 0.75 1 1.25 1.5 y 2.72…

Q: 3 Z Eii %3D From the properties of characteristic equation of strain Zɛ, -Mw -Mw

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Q: (a) Area = ſ dx dy (b) Area = = [[ JJ dy dy dx

A: Follow the procedure given below.

Q: Find dy/dz in terms of e and y if arctan(x®y) = ry°. ||

A: See the details solution in below

Q: dt t In yt

A: Intregate

Q: Evaluate e* dx dy by using trapezoidal and Simpson's rules.

A: Hello. Since your question has multiple parts, we will solve the first integral by first method for…

Q: Find dy if g-s(tant). and t= CostX)

A: Given functions,  y = sin (tan t) t = cos (x) the derivative to find is, dydx = dydtdxdt

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: Reduce the given DE into Bernoulli's equation: dy_y 2x* y-4 - dx 3.

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Q: Evaluate e*y dx dy by using trapezoidal and Simpson's rules.

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Q: Ify arctan (in x), find dx/dy at x = 1/e A B) e/2 e/3 D.

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Q: If y? In(x) = 5, find dy/dx. dy dx

A: This question is based on differentiation with respect to x.

Q: How would I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: dy Yo Calculate dx

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Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: Find the general soulution dy/dx=3y

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Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: Use Laplace Tranformation to solve the IVP.  y'+y=tsint  y(0)=0

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Q: dy Find dx if y = cos e*

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Q: g=ズ, a find dy dx %3D

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Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: eYdx+ costx dy co

A: We have the given equation as   e-ydx+cos2xdy=0   We have to solve this differential equation

Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: dy %3D xp

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Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: then show that dz+z = % dy e te

A: Given:z=ex+yex+eyDifferentiation formula:ddxuv=v.dudx-u.dvdxv2

Q: 1 •arccos y Evaluate esin a dxdy.

A: Find the double integral by using order of change of integrals

Q: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: rc)

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Q: use Gamma Function to evalute the Rollowinq e dy

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Q: Given y=−3cosx, what is dy/dx?

A: y=-3cosx

Q: Find the G.S.of the DE. (ytu dy=D0

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Q: ) dx dy is

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Q: Revers the order and Evaluate= s dx dy y

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Q: Compute: d/dx(arctan(2x))

A: Given

Q: 1. Find by implicit defferentiation dy dx CS wanne+with CamScanne

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Q: when y and u are defined as follows. y = 3u2 + 7   and   u = x2 + 9

A: Here I am attaching image so that you understand each and every step.

Q: dy + y = ť°, dt

A: Given differential equation is: dydt+y=t2 The above equation is linear in y. The integrating factor…

Q: dy 38. dt у сost

A: Given Information: The differential equation is dydt=ycost. Calculation: Calculate the general…

Q: Fined the arc leng th of the curve

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Q: S 6 ttan t dt = %3D dx Jx

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Q: dy dt II

A: