Find f (n) when n = 2k, where f satisfies the recurrencerelation f (n) = f (n∕2) + 1 with f (1) = 1.

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: f(x) = 8+x 8 - x on [4, 6].

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Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Indicate the least integer n for which f(x) is O(x¹) if (4x³+2)(8+3) f(x) = +1

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Q: Let 7 (t) = Find 7 (t) デ'(t) =D<

A: r'(t) =d(r(t))/dt

Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

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Q: If f is invertible and f(- 15) = 6, then %3D | f-(6) and (f( – 15))¯ -1 %3D

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Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: Consider the recursive definition of the function f(n) f(0) = 0 f(n) = 1+ f(n-1) Find ƒ(1), ƒ(2),…

A: Recursive relation: It is an equation which represent a sequence based on some formula. From the…

Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

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Q: G(n) = (d)o(d) is multiplicative function. If p is prime then G(p*), fork >1 equals dịn Select one:…

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Q: Denote owl and wood rat populations in a particular area at time k by xk LK Rk where k is the time…

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Q: If f is invertible and f(4) = 14, then f(14) = and (f(4)) - %3D

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Q: Calculate Sxe 0 re-L₂ (x)L(x)dr by using Recurrence relation of Laguerre function, Ln

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: If f is defined recursively by f(0)=0, f(1)= -2, Find f(3) where f(n+1) =f(n) - 5 x f(n-1)

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