Pblem 1:
Rules are given for encoding a 6 letter alphabet
original letter
|
a
|
b
|
c
|
d
|
e
|
f
|
encoded letter
|
e
|
a
|
f
|
c
|
b
|
d
|
(a) Is the encoding rule a function?
(b) Is the encoding rule one-to-one?
(c) Encode the word ”bad.”
(d) Write a table for decoding the encoded letters and use it to decode your answer to part (c).
(e) Graph the encoding rule and the decoding rule.
(f) What happens if you apply this coding rule three times:
Does f(x) = 3 + sin(x) have an inverse function? Justify your answer.
Problem 3:
(a) What is the viewing angle for the tunnel sign in the figure below?
(b) Use arctangents to describe the viewing angle when the observer is x feet from the entrance of the tunnel.
Problem 4:
Let a = arctan(x) and b = arctan(y). Use the identity
Problem 5:
Find area between the curve and the x-axis
(a) from x = −10 to 10
(b) from x = −A to A
(c) Find the area under the whole curve. (Calculate the limit of your answer in part (b) as A → ∞)
Problem 6:
For θ = cos–1( 1/5 ), find the exact values of (a) tan(θ) , (b) sin(θ) , (c) csc(θ) , and (d)
cot(θ) .
