Let YR(t) = Reit for 0

Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

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Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

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Q: By using the residue theorem, prove that 1 dx 4a3 where x E R, and a >0 is a parameter.

A: Given

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

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Q: 28. Evaluate by Green's theorem (x - cosh y) dx + (y + sinx) dy, where C is the rectangle with…

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Q: 9. If o = F(x, z) dy + G(x, y)dz is a (differentiable) 1- form on R', what can F and G be so that…

A: GIven, ω=F(x,z)dy+G(x,y)dz ⇒dω=∂F∂xdx∧dy+∂G∂xdx∧dz+∂G∂y-∂F∂zdy∧dz Required dω=zdx∧dy+y dx∧dz on…

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: dy for y= In(In(2r')) dt

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Q: t² + 1 t 1 %3D lim→1- h(t) = ?

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Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

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Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: dy Use the formula d.x Ay lim f (x + Ax) - f(x) lim Ax 0 Ax Ax dy when y = 8ª. dx to find %3D dy dx…

A: topic - derivative using limits

Q: Use implicit clifteren tra fion to find * for the fol llving x*y+ 3xy-x = 3

A: The given equation is x2y+3xy3-x=3 To find: dydx

Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: 3. Prove by using the Squeeze Theorem, or otherwise: 1 t2 dt is continuous at 0. T sin t (a) (b) 1+…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: a IRI MAIas. QUESTION 4 xy x2 + y O a.0 lim f(x.y) along the path xy. Let f(x.y) = Find xy) - (0,0)…

A: Solution

Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: - Emluste ihe given limt ké", ut, 177 2. Compute 1he dovivadv'e A she given vactor hu. F()-…

A: Since you have posted 3 questions here, i can answer only first one. Please reupload remaining…

Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: dy If y = tan t , x = tan? t ,Find by using Chain Rule dx at t =

A: Let the two functions are xt and yt. The chain rule to find dydx is given by the following formula.…

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: dy Use the formula dx Ay lim Ar¬0 Ax f(x + Ax) – f(x) lim Ax→0 %3D %3D Ax dy when y = dx 2 to find x…

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Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: Given the eguation y In (x +y + 1) = 8, evaluate dy Assume that the equation implicitly defines y as…

A: Differentiate with respect to x

Q: Evaluate ∮C(yexy−sinx)dx+ (xexy+ 1)dy where C is the path r(t) given by x=t,y=π/2(t−1)2 from t= 0 to…

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Q: what is (x fyx+ fy) given fCKiy)= ey

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Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

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Statements and Logic

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