Weekly Tutorial 4 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 PERMITTED, 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. [8] Evaluate the derivative of the function f(t) = { t + CubeRoot(t + t2) }20 at the point t = -1/2.

a) - (1 + 2/CubeRoot(4))19
b) 0
c) -219
d) This derivative is undefined there

2. [8] Find the equation of the tangent line to the curve described by the function f(x) = {sqrt(20 - x4)}-1 at the point (2, 1/2).

a) y = (x-1)/2
b) y = 8x - 16
c) y = 8x - 31/2
d) y = 3x + 6

3. [8] Evaluate the derivative of the function f(x) = cos4(sin(x))

a) 4 cos3(sin(x)) cos(x)
b) -4 cos3(sin(x)) sin(sin(x)) cos(x)
c) 4 cos3(sin(x))
d) None of these

4. [8] Given that y = tan(sin(t)) and t = sqrt(u2 + 1), then y is a function of u.
Evaluate the derivative dy/du when u = 0.

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

5. [8] Evaluate the derivative of the function h(t) = {(t+2)/(t-2)}3 when t = 3.

a) -300
b) 25
c) 12
d) -68

Total: 40 points

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