Evaluate F. dr where C is represented by r(t). F(x, y) = 7xi + 6yj C: r(t) = ti + V4 - t°j, -2 sts 2 %3D

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: dw dw and ds 3 Assume that w =f(s° +t) and f'(x) = ex. Find dw at dw do II

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Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: (B) The point on the curve r(t)=Dti + (1 + r)j at which r(t) and r'(t) are perpendicular is (1,0).

A: This question is about application of vector calculas

Q: Consider I = f(x)dx. The approximation of i using composite trapezoidal rule with 3 subintervals is…

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Q: 7y f(x, y) = tan a² f dx² dy? dzðy dydr

A: From the given problem:   fx,y=tan-17yx   (a) As we know: ∂2f∂x2=∂∂x∂f∂x So, ∂f∂x=∂∂…

Q: dw Q/Answer the following - ar ,w = (x + 3y + z)², x = r3 – s², y = tan(r + s) ,Fsin(r+s) at the…

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Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take = 3.

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Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: *f(x,y) = xy + aS lšl fry.fyx gl y²+1

A: Given fx,y=xy+eyy2+1

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

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Q: 3. Given: y = f(u) and u = g(x), find dy/dx: а) у %3D cos u, и%3D—х/3 b) у %3D tan u, и%3D 10х — 5…

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Assume that w = f(s3 + t?) and f'(x) = ex. Find dw dw and at ds dw at dw

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Q: Q2 Given z = xw? + cos y + wx , w= t , x = 2t2 , and y = 3t, find dt

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Q: |e*y dx+e* dy; C: r(t) = (t+ 1, ),-1si<3 Exercise 97.

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Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: Find F dX where C is the curve X(t) = ²I+(2t + 1)J, 0<t<5, and F(x.y) = xI+xyJ. %3D %3D

A: First I have written a short note about the line integral along a curve , just use that rule and…

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take a = 3.

A: We have to find the linear approximation of the given function around suitable point.

Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other…

Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

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Q: dy If x = t – sin t and y =1- cost, then find at t = %3D dx a. -2 b. 0 С. 1 d. 2

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Q: b) Find [[F.dS, where S is the top and the side (but not the bottom) surface of the cylinder r + y <…

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Q: CALCULATE I = 2² + y² + z*dædydz, WHERE "T" IS THE CILINDER 2² + y? < 1,0 < z < 1.

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Q5.a) Find if sec?y = x? + t² dt Jsiny dx dy b) Find if tan?y = x² + Jysinx cotx VE2 +1 dt tZ+Idt

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Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

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

Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

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Q: F(x, y) = (e5x sin(y))i + (ex cos(y))j

A: The given vector field is not conservative

Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

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Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: U (d) Let t ==; V at u = x² - y², v = 4xy³. Find- and Əx dy

A: According to our guideline we can only answer first question and rest can be reposted.

Q: h) $ dz =. 1) where C is a positive contour outside of a point z=i= (0,

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Q: dz Q2 Given z = xw? + cos y + wx , w =t, x = 2t2, and y = 3t, find dt

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Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: If f (x, y) = 4e4*cos (y - 1) , then the linear approximation at (0, 1) is %3D (A) 4+ 16x (B) 4+4x…

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: find dw/dx, dw/dy, dw/dz using implicit differentation. Leave your answer in terms of x,y,z,and w.…

A: To find the implicit differentiation of the function: ln(2x2+y-z5+11w)=z...(1) So, take w as a…

Q: Use the variation of parameter method to find a particular solution d²y * + 4y = sec? (2t) Yp of…

A: Consider the provided differential equation,

Q: at at 4) Let t = ,u = x² – y² ,v = 4xy³. Find· ay əx

A: To find: The value of ∂t∂x, ∂t∂y. Given information: t=uv, u=x2-y2 and v=4xy3 Concept used: Quotient…

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: 4 i /," x’dx using four subintervals. Calculate the trapezoid approximation of O T5 = 61.24 O T5 =…

A: Dear user, You need to find step height and using this you need to find endpoints of interval. Then…

Q: Q2 Given z = xw? + cos y + wx , w =t, x = 2t? , and y = 3t, find dt

A: Let's find.

Q: Find (a) PSD of U(t) = X(t) + Y(t) (b) Sxy (@) and SXu (@) %3D

A: Answer: For the given data, we get