Show that the tollawiny ey uation has a solution 9(4) 5.t lim y 4)=9 そ-3 I y't (cos?t) y't (sin t) y =c

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A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: If 7=(x+1)√√x² + yi+tan (3x-y)j and g = y find: fxcurl g+(g.V) at (0,1,1) x + y In(xy+2)+ i+…

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Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

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: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Q1. If f(x.y,z) = cosh²(\x² In y) + tan-(ey*NE) + sec*(sin Vz In x²) Find fx, fy, fz fyx

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: 4. a. Find zx + Zy: given that z(x, y) = tan(x3-3x?y2+2y4) V9-х2-у? b. If u then show that x ди дх…

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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: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: 1. The loop of y = x '(4 - X) 2. y = 6x – x², y = x²– 2x 3. у %3D2х y? + 4x – 8 = 0 4. An arch of y…

A: As per the guidelines we can solve 1 problem only

Q: 1. If H(y) = cos y – sin y, Find H (0), H (),H (1T), and also show that %3D + x) = H (T – x) = -H…

A: Given that H(y)=cosy-siny find H(0), Hπ2, Hπ Show that  Hπ2+x=Hπ-x=-H-x

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

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Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

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: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

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Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

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

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; x = y = 6t t' Enter…

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Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: Find the limits [C cos(4t) – 1 k ´sin(3t) lim t+0 + 4) i+ t sin?(3t) Oi+55/9j+0k e3t 1 i – 2t°j+…

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Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

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Q: Q1. If f(x,y, z) = cosh?(Vx² In y) + tan-(e2y²vz) + sec³(sin vVE In x²) Find fx, fy, fz» fyx

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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: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: s zy dydz こミ0

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: Find y (t) if y – y = 2cos(5t) and y(0) = 0 %3D * (e' – cos 5t + 5 sin 5t) 13 O 1 + (et + cos 5t –…

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Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: in(cos(x)) 2 limy→0

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Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: If 7 = (x+1)√√x² + yi+tan ¹(3x-y)j and g = = y find: fxcurl g+(g.V) at (0,1.4) x + y In(xy +2…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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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: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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