- #1

karush

Gold Member

MHB

- 3,269

- 5

use the definition of continuity and the properties of limits to show that the function is continuous at the given number $a$

$$g(t)=\frac{t^2+5t}{2t+1}\qquad a=1$$

ok i assume we just plug in a for t

$$\frac{1^2+5(1)}{2(1)+1)}=\frac{6}{3}=2$$

theorem 4 if f and g are continuous at a and if c is a constant, then the following are functions are also continuous at a

\begin{align}\displaystyle

&f+g \quad f-g \quad cf \quad fg \quad\frac{f}{g}

\end{align}

$$g(t)=\frac{t^2+5t}{2t+1}\qquad a=1$$

ok i assume we just plug in a for t

$$\frac{1^2+5(1)}{2(1)+1)}=\frac{6}{3}=2$$

theorem 4 if f and g are continuous at a and if c is a constant, then the following are functions are also continuous at a

\begin{align}\displaystyle

&f+g \quad f-g \quad cf \quad fg \quad\frac{f}{g}

\end{align}

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