L(t+1)+L(t-1)
=t(t+1)+1+t(t-1)+1
=t2+t+1+t2-t+1
=2t2+2
so 2t2+2 is corret answer.
Let L:P1 --> P2 be a function defined by L(p)=tp + 1. Where p is a...
Let L:P1 --> P2 be a function defined by L(p)=tp + 1. Where p is a linear polynomial in P1. which of the following is not true? L is a linear transformation L is not a linear operator L is not a linear transformation L is not a 1-1 function
5. Let p and q € P2, and define < p,q >=p(-1)q(-1) + p(0)q(0) +p(1)q(1). (4pts) a. Compute < p,q> where p(t) = 2t – 5t?,q(t) = 4 + t2. (5pts) b. Compute the orthogonal projection of q onto the subspace spanned by p.
Q6) let T(n) be a running time function defined recursively as 0, n=0 n=1 3T(n - 1)- 2T(n - 2), n> 1 a) Find a non-recursive formula for T(n) b) Prove by induction that your answer in part (a) is correct. c) Find a tight bound for T(n).
(2) Let Pn [x] = {p € P[x] : degp <n}, where P[x] is the set of all polynomials. Let the polynomials li() defined by II;tilt - a;) i=0,1,...11 bi(T) = 11: a; - aj) where aj, j = 0,1,..., are distinct real numbers and aia . Show that (d) The change of basis transformation from the standard basis ', j = 0,1,...,n to l; () is given by the Vandermonde matrix (1 00 ... am 1 01 .01 1...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
Let be a function defined by: We define by extension the odd, periodic function of period p = 2 which coincides with the function f (x) on the interval [0, 1]. Draw over the interval [−1, 3] the graph of the function towards which the Fourier series of the odd continuation of the function f (x) converges. f(x) = 1 + x2 pour 0 < x < 1.
3.) Expand the function consisting of a train of pulses of width Tp into Fourier series: (A for – 7 < t < 1 2 f(t) = {o for <t< , lo for the < t < 1 / 1 where T is the period of the function and T, < T.
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f(t)} e-stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0) f(t) 4 (2, 2) 1
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).