Basic Skills 7-14. Derivatives of vector-valued functions Differentiate the follow- ing functions. 13. r(t) = (te", t In t, t cos t)

Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

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Q: Differentiate. f'(t) f(t) cot(t) e e¹(cot(t) + csc(t)²) X

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Q: y" – 7y' + 12y = 3t?e4t – te3t sin t -

A: Given:  y''-7y' +12y =3t2e4t -te3tsint

Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: Find J, ()dx Chint:let Z=Jx)

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Q: Function P(X,y) a In (X*nyt),+tan"() Check the dif ferential equation.

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Q: w = (x^2 + y^2)xy, x = rcosθ, y = rsinθ  a) Use chain rule to find∂w/∂r b) Find ∂w/∂rat the point…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t= 0 T(0) : N(0) =

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Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

Q: 3) y sin-ly² dy

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Q: Q2: Evaluate sin(l₁ t) sin(l₂ t) dt, at: -TT a) 4₁ = 1₂, b) l₁ = 1₂ = 0.

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Q: 9. Find all æ where the tangent line to y = f(x) = sin (x) – sin horizontal.

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Q: y" - √xy = sinx ; (TT) = 0. y' (π) = 11. V" (π) = 3

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Q: if y= Cot" (-+) y=Cot Prove that dy 1-x

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Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: 3.8. Question. Match equations y' = sin x, y' = cos y, y' = y cos(x)· a) c) b) to direction fields.…

A: To find the direction field of a differential equation you first need to isolate y' from the…

Q: 3) y tan-1(y²) dy

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Q: 3 t coso ,3 sin 0 sing dr d0 do /2 0, 0.

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Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

Q: If f(z) = 4z sin z cos z, find %3D f'(z)- Find f'(2) = Question Help: DVideo Message instructor Add…

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Q: 11. V =tr²h (h) constant as A) ans :V' (h) = tr²h 3.

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Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

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Q: Ni cos(2?)a. Cos | x dx

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Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: 2t k, then the distance traveled over 0Sts In 3 is:

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Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: Calculate y' and y" at the point (1, 1) on the curve 5xy² + 8y – 13 = 0. (Give your answers as exact…

A: Given 5xy2+8y-13=0 at 1,1

Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: s-1 The L is (s-1)² – , a) e' sin t b) e' cosh 2t e' sinh t c) e' cosh t d) 2 O b) O d) O a) ()

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