MTH 151

Quiz 2 (corrected)

Fall 2011

Show all work in a neat and organized fashion. Clearly indicate your answers.

20 points possible.

1. (5 pts.) On the attached page, the graph of a function f is given. State the value of each quantity, if it exists. If it does not exist, write DNE.

(a)

lim x→1−  f(x)

(b)

lim x→1+  f(x)

(c)

lim x→1  f(x)

(d)

f(1)

(e)

lim x→3  f(x)

2. (5 pts.) Estimate the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).

lim x→ 2  3x−9 x−2

x=2.1, 2.01, 2.001,

1.9, 1.99, 1.999

3. (5 pts.) Evaluate this limit symbolically, showing all work.

lim x→ 25  5−√x 25x−x2

4. (2 pts.) Sketch a neat graph of a function f that is continuous except for the stated discontinuity.

Discontinuous, but continuous from the left, at 3

5. (3 pts.) Is f continuous at a? Show the work that leads to your answer, using the mathematical definition of continuous.

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