Math 132 - Test #1
Show all work except routine arithmetic computations.
(10 pts) 1. The point P (9, 3) lies on the curve f(x) =
this curve.
√
√
x. Let Q be the point (x, x), also on
(a) Write an expression that gives a general form for the slope of the secant line, P Q.
(b) Compute the numerical value of this slope (to 4 decimal places) for each of
x = 10, x = 9.5, x = 9.25 and x = 9.125. (These may be given as answers
only.)
(10 pts) 2. On the axes provided, sketch a clear picture of a single function satisfying all of these
properties:
(a) f(−1) = 1
(b) lim f(x) = 4
x→−1
(c) lim f(x) = 3
x→2−
(d) lim+ f(x) = 1
x→2
(e) f is continuous on (−1, 2]
(20 pts) 3. Show a step by step calculation of the following limits. You may combine any needed
use of the Limit Laws into a single step.
3x2 − 2
x→−∞ 5x − 7x2
(a) lim
(b) lim−
x→3
|x − 3|x2
x−3
Math 132, Exam #1
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(10 pts) 4. On the axes provided, sketch a graph of


if x ≤ −1
2
f(x) = x2
if −1 < x ≤ 1


x − 1 if x > 1
(10 pts) 5. The figure shows the graph of a function named f
with asymptotes marked as dashed lines.
(a) Express, in correct limit language, all the
asymptote relationships in the graph.
(b) Write the equations of the aysmptotes.
3
-5
5
-3
x
is shifted left by 4 units and then upward by 3
x2 + 1
units. What is an equation for the new, shifted graph?
(10 pts) 6. Suppose that the graph of y =
(10 pts) 7. Solve the equation 23x+1 = ex for x. Show your method. Give the answer both in exact
form and as a decimal approximation.
Math 132, Exam #1
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(10 pts) 8. Consider the parametric equations of a curve; x = 2t − 1, y = 1 − 2t, −3 ≤ t ≤ 2.
(a) Eliminate the parameter to find the Cartesian
equation of the curve.
(b) Sketch the portion of the curve as described
on the axes given.
x2 + 2x − 3
. Showing all use of Limit Laws,
x−1
evaluate lim f(x). Also, sketch a complete graph of y =
(10 pts) 9. Let f(x) =
x→1
f(x) on the accompanying axes.