Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: The volume of the cylindrical shell is given by V=2πrh∆r, where ∆r is the thickness of the shell.…

Q: Calculate the total differential dz for z = r sinh(ry) + yelv

A: Note- since you have asked multiple questions, So Acc. to Bartleby guidelines we are supposed to do…

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Q: Find the differential of the function w=x^5sin⁡(y^5z^4) dw=  dx+  dy+  dz

A: Differential of a function is simply the derivative of a function. Also, d(uv) = u.dv + du.v

Q: •12 Evaluate the integral dx dy by reversing the 3 order of integration.

A: To evaluate: The integral of ∫012∫y34ex2dxdy by reversing the order. Explanation: Consider the image…

Q: 6. Evaluate: dædy Hint: Use dydx as order of integration.

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Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

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Q: evaluate using Integration by Parts.

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: Find the total differential dz for z=tanh(y)ln(x)

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Q: dx 3. J TxVx-1

A: the given integral is: ∫dxxx-1 we have to evaluate the given integral.

Q: Integral in REVERSE ORDER

A: Given that  I=∫08∫y32ex4dx dy Limits are given y=0 and y=8     x=y3y=x3  and x=2

Q: Evaluate the double integral : (3 – 8z) dz dy

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Q: 4-x? Change the order of integration | | f(x, y, z)dzdydx in the order dydxdz.

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Q: use the elimnaton method zhみみ人みメ differential equeti cns

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Q: What is the integrating factor of xy' + 6y = 3xy3?

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Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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Q: .2 What is the reversed order of integration of 1 dxdy? a. II Vx* +1 dydx 0, O b. x4 +1 dydx 0, .8…

A: Topic:- application of integration

Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

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Q: integral t 3 et dt

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Write the approximate change formula for a function z = ƒ(x, y) at the point (x, y) in terms of…

A: Consider the following function: z=fx,y

Q: he integra = 3/2 is dz Z-2

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Q: 2: Change the order of integration. •ln 4 f(u, у)dydx.

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Q: Find the total differential. z = 10x6y7 dz = %3D

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Q: TO Show Jv - x-V そーレ V+ dx

A: Jvx = ∑m=0∞ -1mx22m+vm! m+v!

Q: integral from -1 to 1 of arccos (y) dy

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Q: Find the total differential of z= f(x, y), where f(x, y) = In Use * for multiplication of variables,…

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

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Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Find the total differential. z = ex tan(y)

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Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Given: length,h=20 cmd=6 cmdr=0.001dV=?

Q: Find the particular integ rel of This differential etuatim. (40²+HD+= 2e +8x %3D

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Q: I Eliminate the arbitrary constants 1. X = y=at + bt² - Int,

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Q: Evaluate. (use C for aonstant of intgration) dx 2 X "- 3

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Q: Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

A: Given information:- Find the work done in stretching a spring of natural length 8 cm, from 10 cm to…

Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

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Q: 1. Evaluate LL vsin(a*) dx dy by first changing the order of integration.

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Q: What is the (a). general solution to xydx-(x+2) dy=0? (b) integrate.

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Q: Find the limits of integration with respect to u and v

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Q: FCx) is continoos on L3,5) and S Fex) dx= 5 Evaluate integral

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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Q: 4) First make a substitution and then use integration by parts to evaluate the integral. (Use C for…

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Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

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Q: et * e-t Compute the convolution integral.

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