c.) 3 (1+1) dy = 2ry (y" – 1) dz d.) (z+1) +(* +2) y = 2ze e.) 2y dy - (3y cot z+ sin z cos z) d

Q: dy ecos (2t). Find an expression for -for Consider the parametric curve x (t) = -esin (3t) and y (t)…

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Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

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Q: Q5: a. Find * and for u - p=x+y+z ,and q = x+ y+ z, and r=x+y-z, at the point (x,y, 2) = (v3, 2,1).…

A: a)                          u=p-qq-r                             p= x+y+z;…

Q: y = In x3 sinx 2 Cx² + 4

A: The function is given by y = lnx3sinxx2+4 To evaluate: The expression of dydx.

Q: | cos r In(sin z)dr

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Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

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Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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Q: O1) Prove that: [Answer only two du dx (A) - tanh u = dx 1-u du (B) u-1 = sec u+C >1 2. (C) cscx =…

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Q: y2 +Cos f (x, y, z) =

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Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

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Q: A point starts at (x, y) = (6,0) and moves CCW along a circular path centered at (x, y) = (0, 0).…

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Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: Q. Suppose a vibrating string is governed by the equation f (x, t) = 2 cos(5t) sin x, where x is the…

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: Let y be the hypocycloid R(t) = (8 cos³ t, 8 sin³ t), t = [0, 27], and C the portion of Y from the…

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Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: if z = cos20, and 0 = [cot(w) + 1] - %3D rcotx sint Find if cot?y = x² + Sy2sinx dx

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Q: ミe さ 号

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Q: Prove that (1-x*)у ,-ху, +р'у-0

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Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.

Q: The curves F₁ (t) = (2 sin(t), 4 cos(t), e7t) and 72(t) = (3 ln(t), 4√t, t³) intersect at the point…

A: The angle between two curves is the angle between their tangents at the point of intersection .

Q: Evalate jsinty)hube where 2 05ys1,05xsy. a) 1-cos(r) b-costr)) 9-cosd) osd) d) 1-cos(l))

A: Change of variables:             ∫x1x2∫y1y2f(x,y)dy dx=∫y1y2∫x1x2f(x,y) dx dy.

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

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Q: Suppose z = f(x, y) = (x² + 2) sin(y) + xy². By setting one variable equal to a constant (either x =…

A: Given surface is,This equation represents a surface in three-dimensional space.To find the:

Q: (5 + sin r)e 2. If y = what is dy/dr? 12 - 7

A: Use basic identities of derivatives.

Q: Find for the following functions: - dx 1) y = (cos x)V 2) y = sin x* + e!nx 3) y = 7cos/2x+3

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Q: ⑤ 2 COSX . dx R=4 3 Sinh lex)dx sinh R=4 7 2 2 e FR=4 0

A: Note: You didn't mention the method from which question is being solved. So, I does the question…

Q: dy for the parametric curve x= 2e', y= sin(1 + e' ) dx Find

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