Weekly Tutorial 2 for Math. 69.107A,
Elementary Calculus I

Instructor: Dr. Angelo Mingarelli

Notes: These are group tutorials; each question is to be divided among the group (at most 5 students in a given group), solved and submitted to the T.A. at the end of the 50 min. period. NO NOTES ALLOWED, only group interaction...All students within a group will be assigned the same grade for this tutorial...
This online test is meant to be printed and handed in.
Solutions will appear later on during the term ...

Group names (Please PRINT) & Student Numbers:

1. Use Newton's method to calculate an approximation to a root of 2 sin(x) - x.

Start with xo = Pi (=3.14159...) and perform 4 iterations.

a) 2.094394
b) 1.895494
c) 1.965743
d) 1.789652

2. Find the derivative of the following function

f(x) = tan{ x2/ sqrt(x2 + 4) }

at x = 0 .

a) 1
b) 1/4
c) 0
d) 1/8

3. Use the Rule of Bernoulli-L'Hospital in order to evaluate the limit:

limx -> 0 [cos(6x) - cos(4x) ]/ x2

a) -2
b) 10
c) 2
d) -10

4. Find the slope of the tangent line to the function f given by

g(z) = z / sin2(z)

at z = Pi/2.

a) 1
b) -1
c) -2
d) 0

5. Use the Rule of Bernoulli-L'Hospital in order to evaluate the limit:

limx -> infinity { x sin(1/x) }

a) 0
b) 1
c) The limit does not exist
d) -1

Click and hold for solutions:

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