Weekly Tutorial 2 for Math. 69.007A,
Introductory 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. NOTES ALLOWED, along with 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. Let xn = n / (n+1), n = 1, 2, 3, ...

How big must the subscript n be in order that | xn - 1 | < 1/1000 ??

a) n > 999
b) n > 99
c) n > 998
d) n < 999

2. Determine whether or not the sequence yn = (-1)n/n converges to a limit. If so, find it.

a) Yes, it converges to 1
b) Yes, it converges to -1.
c) Yes, it converges to 0.
d) No, it doesn't converge.

3. Evaluate the limit:

lim x -> o{sin(3x) - sin(4x)}/2x

a) 3/2
b) -1/2
c) 1/2
d) 1

4. Let c be a constant. A function f is defined as follows:

f(x) = x+c, for x < 2 and f(x) = cx2 + 1, for x > 2.

What value must the constant "c" have in order that f is continuous at every real number?

a) 3
b) This can't be done!
c) 1/3
d) -1

5. Evaluate the following limit:

limy -> 8{[y - 8] / [CubeRoot(y) - 2] }

a) 6
b) 2
c) 4
d) 12

Solutions are given within the box: