Lw(s) ~ 1 – Show that 1 is MTTF where

Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: S (9x – 4) dæ. -2

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Q: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: If | h(t)dt = 24 %3D and 8 |h(t)dt = 10.6 what does the following integral equal? h(t)dt- %3D

A: We know, ∫abf(x) dx = ∫acf(x) dx + ∫cbf(x) dx         (if a<c<b)

Q: .rdx dy Prove that (a) (b) (8)

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Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 2. Calculate the divergence of D = (÷)[10xyzảy + 5x²zãy + (2z3 – 5x²y)ã,] at P(-2,3,5).

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Q: dw Use an appropriate form of the chain rule to find dt w = In(162? – 4y + 3z³); 1 = ti, y = tỉ,…

A: Topic- differentiation

Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: 0. dy for y = 4t dt. 4t +1 3x3 Use Leibniz's rule to find хр

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Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: Let y = 5x + 7x + 3. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay =

A: Follow 2nd step.

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: Suppose that a duck is swimr - perature is given by the formı v²sin x. Find dT/dt in two chain rule…

A: Given query is to find the derivative of function T.

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given DE is 2x2xdx+ydy=8xdy-ydx..........(1) We have following formulae, dyx=xdy-ydxx2 and…

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: If L = sqrt(x2 + y2,) dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 12.

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Q: Let y = 2x + 5x +. 2. If Ax = 0.4 at a = 4, use linear approximation to estimate Ay Ay =

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Q: Evaluate the integral: ∫ t2 sec2(9t3 + 1) dt

A: The given integral is, ∫t2 sec29t3+1 dt. Apply the u-substitution by taking u=t3. Then dudt=3t2.…

Q: Evaluate the integral | t(sec t2)4 dt

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Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Sketch the slope field for dy dt = t y for −2 ≤ t ≤ 2, −2 ≤ y ≤ 2.

A: Sketch the slope field:  dydt=ty for -2≤t≤2, -2≤y≤2. Construct the table of Values. t y dydt 0…

Q: Find dy/dt. Show all work. y= t^3(t^3+2)^6

A: the given function is: y=t3t3+26  we have to calculate dydt.

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: compute J secx dr. I n trying to integrate

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Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

Q: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

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Q: Find the lineanzation LlXiy) of f (iy) =x*-5Xy at (2,1). Then use the linearization to approximate f…

A: Here in this question we need to linearize the given function and then approximate the value of…

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

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Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Use by exact form

Q: Let y = 3x +7x+ 4. If Ax = 0.4 at a = 1, use linear approximation to estimate Ay %3D Ay 2

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Q: find the volue of the od specify ingrol integrol T-x2 the

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Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

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Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…