Fit a quadratic function of the form ?(?)=?0+?1?+?2?2 f ( t ) = c 0 +...

Fit a quadratic function of the form ?(?)=?0+?1?+?2?2 f ( t ) = c 0 + c 1 t + c 2 t 2 to the data points (0,−1) ( 0 , − 1 ) , (1,8) ( 1 , 8 ) , (2,−7) ( 2 , − 7 ) , (3,−6) ( 3 , − 6 ) , using least squares.

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6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for −...

6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for − 1 ≤ t < 0 0 for t = 0 1 for 0 ≤ t < 1 0 for 1 ≤ t ≤ 2 can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t <...

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t < L is given. Find the Fourier cosine and sine series of f and sketch the graphs of the two extensions of f to which these two series converge

1. Express the function f(t) = 0, -π/2<t<π/2 &nbsp

1. Express the function f(t) = 0, -π/2<t<π/2 = 1, -π<t<-π/2 and π/2<t<π with f(t+2π)=f(t), as a Fourier series.

Let f: [0 1] → R be a function of the class c ^ 2 that...

Let f: [0 1] → R be a function of the class c ^ 2 that satisfies the differential equation f '' (x) = e^xf(x) for all x in (0,1). Show that if x0 is in (0,1) then f can not have a positive local maximum at x0 and can not have a negative local minimum at x0. If f (0) = f (1) = 0, prove that f = 0

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2 if t>=3 }

Part A: Express the quadratic function in standard form (vertex form). ?(?) = 1 − 12?...

Part A: Express the quadratic function in standard form (vertex form). ?(?) = 1 − 12? − 4? 2 Part B: Find the quotient and remainder using synthetic division. ?^4 + 2?^3 − 10? all over ? − 3 Part C: A stone is thrown upward from the top of a building. Its height (in feet) above the ground after t seconds is given by the function ℎ(?) = −16?^2 + 96? + 48. a. What maximum height does the...

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Fit a quadratic function of the form ?(?)=?0+?1?+?2?2 f ( t ) = c 0 +...

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