Find the radius and convergence of the following: ∞ χη Σ (n!) η=1

Q: Find the trigonometric Faurier Series of the function defined by; flx) = x + # if = < X <... -T..

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Q: A particle moves along a number line with velocity at time t given by the formula v(t) = t ln(t +…

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Q: Solve the following ODE using Laplace under the following initial conditions d²y 1 Y(0) 3 dy dx = 0…

A: The differential equation is:We have to solve the given differential equation by Laplace transform.

Q: Given the functions Ax). and g(x) = determine the value of - COS X 10+x %3D 03 O 11 O V11

A: we are given f(x)=cosx,  g(x)=10+x and we need to find the value of the composition function g(f(x))…

Q: Solve the following ODE subject to the initial condition y(0) y? – 22 x² – 22 calculate y(1/4).

A: Solution for the ordinary differential equations: With initial condition y(0)=1. Calculate y(1/4).…

Q: A chord of a circle is a line segment connecting two points on the circle. To pick a point uniformly…

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Q: Find Tη centered at x = a for all n. n f(x) = e*, a = -6 Τη (Χ) = Σ j = 0 n

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Q: 2 s 0 x dx

A: n  = 4

Q: In this problem you will evaluate x dx using the 4 methods discussed in class. a) Estimate the value…

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Q: (x² + y²)dx + (2xy + cosy)dy = 0 %3D

A: Given differential equation is  (x2+y2)dx+(2xy+cosy)dy=0 we have to check if it is exact then solve.

Q: Solve the following ODE proble using Laplace. [Ignoring units for simplicity] The average…

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Q: 8- Solve ihe separation of variable MeRod satisfy %3D The condilion as tp0 as for x=0 and a =a T=メ…

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Q: 5 cos 30 lim 0-т 6 сos(-20) б coS

A: The given limit expression is limθ→π5cos3θ6cos-2θ.

Q: Q.No.7.: Using residue theorem, evaluate: dz (2° +4)* dz, c: z-i=2. tion/

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Q: Let f,x cos(x) dx. The approximation of I using the two-point Gaussian quadrature !! formula is: O…

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Q: Evaluate using Simpson's rule for n = 4 to 4 decimal places: n = 8 to 4 decimal places: n = 16 to 4…

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Q: dy 5y dt Given the ODE: 1 Find the upper limit on At for this ODE to 3 decimal places. (At<?) 2…

A: Given: dydt=-5y

Q: (b) Find all times t in the interval 0 < t < 3 when the particle changes direction. Justify your…

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Q: 10. Find mAD (11r – 3) B (8x + 15) A %3D Measure of Arc AD =

A: Given: ∠ABD=11x-3° and ∠ACD=8x+15° The objective is to find the measure of Arc AD

Q: Solve the following over the interval [0, 27]; Sin 2x Cos *- Sin x = 0 O 0, 0, 6 O 0, 7, 2m, , O 0,…

A: Given sin2xcosx-sinx=0 The trigonometric identity used is sin2x=2sinxcosx So the expression becomes…

Q: 1.33 The velocity (m/s) of a body is given as a function of time (seconds) by ds = v(t) = 200ln(1+…

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Q: What is the Riemann sum that represents the illustration shown? The function is f(x)=√√x. 3 i=1 3 Σ…

A: Riemann Sum Let f(x) be defined on the closed interval [a, b] and let P be a partition of [a, b]…

Q: 21 o (z) = of the nth mode is cos for all n n² for odd n and 0 for even n n² for even n and 0 for…

A: Sol

Q: (e) Use Euler's formula to prove the following formulas for cos(r) and sin(x) : eiz + e-iz eiz –…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: on 5olve ODE g(0)=100 ais the guantity over time what is Q 70 at t=1 second tor ķ =-0,8 secods

A: Here, Q’(t)=k(Q-70) where k=-0.8 and q(0)=100.

Q: En=1" Vn sin а. 1 b. 2 c. Converge

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Q: Consider a surface S:Z = (x-1)'+2 in the first octant limited by y=-4x(x-2) sShawn ju the figere. z…

A: We will construct the appropriate surface integral to solve  the question