Please follow the following order: G = < N, T>, N = {E, T, F}, T = { i, n, (, +, -, *, /, ) }
FIRST(E') = FIRST(E) = FIRST(T) = FIRST(F) = {i,n,(}
FOLLOW(E') = {$} =>[Start Symbol]
FOLLOW(E) = {+,-,),$} =>[Since E
is right most in E'->E, FOLLOW(E) contains FOLLOW(E')]
FOLLOW(T) = {+,-,),$,*,/} =>[E->T => FOLLOW(T) contains
FOLLOW(E)]
FOLLOW(F) = {+,-,),$,*,/} =>[T->F => FOLLOW(F)
contains FOLLOW(T)]
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
For some n > 1, let T E End(Pn) be given by T(p) = p'. Show that T is not diagonalizable.
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
27? 73 S2 0.20A 0.001Fv(t) i(t) -10t The capacitor voltage in this circuit is v(t)- 14.60-33.6 efort 0. -10t The current in the 73-? resistor is represented as ,(t)-E+ Fe - for t > 0. Determine the values of the constants E and F: V and F V.
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
3. Consider a function F(t) which is zero for negative t, and takes the value exp(-t/2 ) for > 0. Find its Fourier transforms, C(w) and S(w), defined in 200 F(t) = C(w) cos(wt) dw + Sw) sin(wt) do. J-00 J-00 [Hint: Use Euler's theorem.] 4. Demonstrate that Sr?)dt = 2* ["icºw) +8?(]dio, J-00 J-00 where the relation between F(t), C(w), and S(w) is defined above. This result is known as Parseval's theorem.
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.
Find the Laplace Transform of f(t)= -1 if t <= 4; f(t) = 1 if t>4 Find the Laplace Transform of f(t) = - 1 ifts 4; f(t) = 1 if t> 4.
Consider the following recursive definition: if n=1 F(n)= | Fin - 1) +2 if n > 1 (O What set describes this definition? OOOO The set of nonnegative odd integers The set of even integers The set of nonnegative integers The set of odd integers none of the above The set of nonnegative even integers
I need help with these Laplace problems:) (1 point) Find the Laplace transform of <9 f(t) = { 0, " I(t - 9)?, 129 F(s) = (1 point) Find the inverse Laplace transform of e-75 F(s) = 52 – 2s – 15 f(t) = . (Use step(t-c) for uc(t).) (1 point) Find the Laplace transform of 0. f(t) t<5 112 – 10t + 30, 125 F(s) =