Here are three videos (total run time about 23 minutes) and two short Maple scripts on the topic of Limits.

Introduction to Limits (Part 1). Definition. Examples.

 

Introduction to Limits (Part 2).  Examples.

 

Introduction to Limits (Part 3) – More examples.

 

Here is the Maple code to solve the limit problem
$$ \lim_{x \rightarrow 5} \dfrac{(3x + 1)(x – 5)}{2x(x-5)}$$ from the above videos. The Maple script also graphs $f(x) = \dfrac{(3x + 1)(x – 5)}{2x(x-5)}$.

 f := x -> ((3*x + 1)*(x - 5))/(2*x*(x - 5));
Limit(f(x), x = 5) = limit(f(x), x = 5);
plot(f(x), x = -1 .. 6, thickness = 4, gridlines, size = [800, 800], title = typeset("f(x) = ", f(x)));
# End of Maple Script

Here is the output of the above script.

 

Here is the Maple code to solve the limit problem
$$ \lim_{x \rightarrow 3} \dfrac{x^2 + 9}{x^2-8x+15}$$ from the above videos. The Maple script also graphs $f(x) = \dfrac{x^2 + 9}{x^2-8x+15}$.

 f := x -> (x^2 + 9)/(x^2 - 8*x + 15);
Limit(f(x), x = 3) = limit(f(x), x = 3);
plot(f(x), x = 0 .. 4, thickness = 4, gridlines, size = [800, 800], title = typeset("f(x) = ", f(x)));
# End of Maple Script

Here is the output of the above script.