The answer is given below

Demi-Leigh Barrera

Answered 2021-05-18
Author has **24846** answers

content_user

Answered 2021-09-28
Author has **10829** answers

A function f is continuous from the right at x=a if

\(\lim_{x\to a^+}f(x)=f(a)\)

And f is continuous from the belt at x=a if

\(\lim_{x\to a^-}f(x)=f(a)\)

f is said to be continuous when it is continuous from both left and right

\(f(x)=\begin{cases}\frac{1}{x+2}&if\ x\ne-2\\1 &if\ x=-2\end{cases}\)

So we can see that:

\(\lim_{x\to-2^-}f(x)=-\infty\)

And

\(\lim_{x\to-2^-}f(x)=+\infty\)

Bat \(f(-2)=1\)

Therefore fis discontinuous at x=-2 from both left and right

Result: f is discontinuous at x=-2 from both left and right

asked 2021-01-30

\(2y'+y=0 , y(0)=-3\)

a) \(f{{\left({t}\right)}}={3}{e}^{{-{2}{t}}}\)

b)\(f{{\left({t}\right)}}={3}{e}^{{\frac{t}{{2}}}}\)

c)\(f{{\left({t}\right)}}={6}{e}^{{{2}{t}}}\)

d) \(f{{\left({t}\right)}}={3}{e}^{{-\frac{t}{{2}}}}\)

asked 2020-10-26

Given \(f(t)=-\frac{1}{2t}+8 , 0\leq t<4 , f(t+4)=f(t)\)

Find \(F(s)=L\left\{f(t)\right\}\) of the Periodic Function

asked 2021-02-21

\(u_t=u_{xx} 0<x<1 \text{ and } t>0\)

\({u}{\left({x},{0}\right)}= \sin{{\left(\pi{x}\right)}}\)

\({u}{\left({0},{t}\right)}={u}{\left({1},{t}\right)}={0}\)

asked 2020-11-22

\(\begin{cases}t & 0,4\leq t<\infty \\0 & 4\leq t<\infty \end{cases}\)

\(L\left\{f(t)\right\} - ?\)

asked 2020-11-08

Express f(t) in terms of the shifted unit step function u(t -a)

F(t) - ?

Now find the Laplace transform F(s) of f(t)

F(s) - ?

asked 2021-09-24

Explain why the function is discontinuous at the given number a. Sketch the graph of the function. \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}+{2}}}}\) if \(\displaystyle{x}\ne{q}-{2}\)

a= -2

1 if x = -2

asked 2020-12-27

\(\displaystyle f{{\left({t}\right)}}={\left\lbrace\begin{matrix}{1}-{t}&{0}<{t}<{1}\\{0}&{1}<{t}\end{matrix}\right.}\)