Q. Determine whether the given functions are exponentially bounded and piecewise continuous on 0 ≤ t...

Question

Question

Q. Determine whether the given functions are exponentially bounded and piecewise continuous on 0 ≤ t < ∞.

(a) f(t) = tant

(b) f(t) = cosh2t

(c) f(t) = $\left \lfloor t \right \rfloor$ , where $\left \lfloor t \right \rfloor$ denotes the greatest integer less than or equal to t.

math Advanced-Math

Answer 1

Answer #1

ie, at -2t e+ e 2 - Kt > 1. [96) = 1] . - cosh (2)> kt+1 Thus we see that for Sufficiently har large tyo Cosh (at) & a kt for

Answer 2

Similar Homework Help Questions

consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)d...

consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)ds We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image tg p(s)ds
Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that...

Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that T is positive if and only if = (here 1 denotes the constant function [0, 1] → R, x → 1). We were unable to transcribe this imageWe were unable to transcribe this image
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x,...

a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...

find the solution of the inhomogeneous system for y" +p(t)y' +q(t)y = f(t), a second order...

find the solution of the inhomogeneous system for y" +p(t)y' +q(t)y = f(t), a second order scalar equation with p, q, f continuous on interval I, for which (to ) = 0, to on I We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A metric space (X, d) is totally bounded if, given ε>0, there exists a finite subset...

A metric space (X, d) is totally bounded if, given ε>0, there exists a finite subset = of X, called an ε-net, such that for each x∈X there exists ∈ such that d(x,) < ε. Prove that if Y is a subset of a totally bounded space X then, given ε>0, the subset Y has an ε-net and therefore Y is also totally bounded. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
TIMER Chapter 6, Section 6.1, Question 01 Determine whether f is continuous, piecewise continuous, or neither...

TIMER Chapter 6, Section 6.1, Question 01 Determine whether f is continuous, piecewise continuous, or neither on the interval Osts 3. (2+² Ostsi f(t) = 5+t, 1<ts2 9-t, 2 <ts 3 piecewise continuous neither continuous

The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t>...

The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t>...

The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
Where Let n(t) be a fixed strictly positive continuous function on (a, b). define H, =...

Where Let n(t) be a fixed strictly positive continuous function on (a, b). define H, = L([a,b], 7) to be the space of all measurable functions f on (a, b) such that \n(t)dt <0. Define the inner product on H, by (5,9)n = [ f(0)9€)n(t)dt (a) Show that H, is a Hilbert space, and that the mapping U:f →nif gives a unitary correspondence between H, and the usual space L-([a, b]). We were unable to transcribe this image

A current passing through a resistor (R = 16 Ω) decreases exponentially with time as I(t)...

A current passing through a resistor (R = 16 Ω) decreases exponentially with time as I(t) = I0e-αt where I0 = 7.5 A and α = 0.25 s-1. Calculate the total energy dissipated by the resistor in joules as time goes to infinity. E(t→∞) = Calculate the energy dissipated by the resistor in joules during the first 5 seconds. E = We were unable to transcribe this imageWe were unable to transcribe this image