Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: dw Find if w = xy + z,x = cost, y sint and z =t at t = 0. dt

A: In the given question, the concept of the derivative is applied. Derivative We can use a derivative…

Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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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: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

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Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: Find dy at taal dt and ya Vltx? and X = t.

A: Explanation of the solution is given below...

Q: Assume that y=2x and dx/dt =4. Find dy/dt . dy/dt

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Q: The integral. 1 dydx is VÆ V10 – y3

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Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Given the function ƒ (x, y, z) = V7y – 3x³ z, calculate the partial derivative with respect to y, in…

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Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Find dw/ds and aw/at using the appropriate Chain Rule. Function Point w = sin(5x + 6y) X = s + t, y…

A: According to guidelines we solve only first three parts.

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

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Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: find the general salution of ly-3y12)de = xdy,

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Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: Suppose that w = xe"/, where x = t², y = 1 – 6t, and z =1+ 4t. dw Find dt

A: w=xeyz, where x=t2 , y=1-6t and z=1+4t

Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

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Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

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Q: Find y Ly imelicit differen -tiation, VスナUゾ 21

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Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z =t², (0 <t< 1).

A: As per the question we are given a line integral, which we have to evaluate around the curve C.

Q: Let y = 5x + 4c +3. If Ar 0.1 at z 5, use linear approximation to estimate Ay

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Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: Assume w = x²y*, where x and y are functions of t. Find dw/dt whenx = 3, dx/dt = 2, dy/dt = 4 and y…

A: To find the derivative of the given function w,  we need to apply chain rule of differentiation and…

Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

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Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

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Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

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Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the…

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).