Math 1210
Quiz 3
January 24th, 2014
Answer the following three (3) questions. Every question is worth the same.
You may use scratch paper, but you can only turn in this sheet. Please
justify your answer in the space provided: writing the solution without any
explanation is not enough. No cell phones, calculators, notes, or music
players are allowed during the quiz.
Name:
UID:
√
1. Consider the function f (t) =
t−1
.
(t−1)(t+1)(t−2)
(i) What is the domain of f (i.e. where is f defined?)
(ii) At which points is the function discontinuous? Are the discontinuities removable /
jumps / vertical?
(iii) For every removable discontinuity, find the limit.
(iv) For every jump or vertical discontinuity, find the corresponding one-sided limits.
2. State the intermediate value theorem and use it to show that the equation (cos t)t3 +
6 sin5 t − 3 = 0 has a solution between t = 0 and t = 2π (you don’t have to find the
solution, just show that there is one).
3. Find the slope of the tangent line to the curve y =
1
x−1
at the point (0, −1).
Recall that if a curve is given by an equation y = f (x), the slope of the tangent line at
a point (c, f (c)) is given by the limit
f (c + h) − f (c)
h→0
h
lim
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