Question

use definition of derivative: G(t)= 1-2t/3 +t

Answer 1

\[f(t) = \frac{1-2t}{3+t}\]
By the limit definition of the derivative,
\[\begin{align*}f'(t)&=\lim_{h\to 0}\frac{f(t+h)-f(t)}{h}\\\\\\
&=\lim_{h\to 0}\large\frac{ \frac{1-2(t+h)}{3+(t+h)} - \frac{1-2t}{3+t} }{h}\\ \\\\
&=\lim_{h\to 0}\large\frac{ \frac{1-2t-2h}{3+t+h} - \frac{1-2t}{3+t} }{h}\\\end{align*}\]
Can you take it from here?

Answer 2

thanks so much...yes i can