Find the length of the helix traced by 7(t) = a cost i + a sint j+ct k,a >0,0 sts 2n %3D (a) 2n (b) ¤(a² + c?)/½ (c) 2m(a² – c²)/½ (d) 2m(a² + c?)/½

Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

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Q: Find the arclength of y = 2x + 3 on 0 < x < 3

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Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

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Q: Find the mass of a thin wire shaped in the form of a helix, r(t) = ( 3 cos t, 3 sin t, 4t) with 0 <…

A: The curve is given by  rt=⟨3cost,3sint,4t⟩ , 0≤t≤3π2                   (i) Then,…

Q: below by Solve the differential equetion using using the method af reduction of ordes y" - 3y +2y 2く…

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Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

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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: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

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Q: Use the Quadrature Rule Calculate I = S e2x dx using the 3-point Gaussian Quadrature method.

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

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: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

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Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

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Q: dy In(5a + 2) Find for y = %3D dx

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Q: au +20 dy 10 www ax dy dy?

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Q: Find the arclength of y = 4x + 3 on 0 < x < 2

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Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

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Q: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…

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Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

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Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Find the point on the curve F(t) - (5 sin t)i + (5 con t)j+ 12tk at a distance 20 units along the…

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Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

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Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: Find the total differential. w = e7Y cos(4x) + z7 dw

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Q: Integrate to find the length of the curve. 8 S = 2 - + 4t dt 4 + 8 2t ++) dt = (? +t ln(t) 1 II

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Exponential Growth Model

The relation that represents an exponential function is: