Unformatted text preview: Project 6
1. Examine the piecewise-deﬁned function below, and sketch the graph carefully on the axes: g (x) = 2 1+x 0 2− 1 x 1 x<0
x>1 Evaluate the following limits:
lim g (x) = −∞ lim g (x) = 1 x→0− x→0+ lim g (x) = 1 lim g (x) = 1 x→1− x→1+ 2. Sketch the function h(x) = lim g (x) = DNE x→ 0 lim g (x) = 1 x→1 x2 − 6x + 5
x−5 What polynomial function is identical to h(x) for all x except x = 5 ?
Evaluate the limit: lim h(x) .
x→ 5 limit :4
What special feature does the graph of h(x) have?
3. The Heaviside function H (x) is a very simple but useful function in the natural world, deﬁned
as shown below. Sketch the graph of K (x) = 1+3H (x − 2) on the axes provided, and evaluate
lim K (x) = 1 x→2− H (x) = 0 x<0 1 x≥0 lim K (x) = 4 x→2+ lim K (x) = DNE x→2 Note K (x) = 4 when x ≥ 2, and K (x) = 1 when x < 2. ...
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