ESP 1206 Problem Set 22
Definitions:
1) y  tan 1 x if and only if y is the angle (or number) between -/2 and /2 whose
tangent is x.
2) y  sin 1 x if and only if y is the angle (or number) between -/2 and /2 whose sine
is x.
3) y  cos 1 x if and only if y is the angle (or number) between 0 and  whose cosine is
x.
4) y  sec 1 x if and only if y is the angle (or number) between 0 and /2 or between /2
and  whose secant is x.
Domains and Ranges:
  
Range:  , 
 2 2
  
1
2) y  tan x Domain: (-,)
Range:   , 
 2 2
1
3) y  cos x Domain: [-1,1]
Range: [0,]
1
4) y  sec x Domain: (,1]  [1, ) Range: [0,  / 2)  ( / 2,  ]
1
1) y  sin x Domain: [-1,1]
Note: arcsin x = sin 1 x , arctan x = tan 1 x , etc.
1
. This is blatantly false,
sinx
would show no understanding of the inverse trig functions, and would cause Prof.
Agud great emotional stress were she to see something like this on your paper!!!
Note: DO NOT EVER WRITE, for example, sin 1 x 
Problems:
I) Fill in the blanks:
1) arcsin (-1) = _____
3) arccos (-1/2) = ______
5) tan 1 3 = _______
7) arcsin (sin 2/3) = ______
9) sin(sec 1 ( x / 4))  _____
2) arctan (tan 5/4) = ______
4) sin (arctan x2) = ________
6) cos ( sin 1 x 3 ) = __________
8) arccos (cos 5/3) = ______
10) cos(sin 1 (2 y / 3))  _________
11) tan (sec-1 (3y)) = _______
12) sin tan 1 x 2  2 x , x  2 = _______


RECALL:
f ( x)
  then f(x) grows faster than g(x).
g ( x)
f ( x)
2) If lim
 0 then g(x) grows faster than f(x).
x  g ( x )
f ( x)
3) If lim
 L  0 then f(x) and g(x) grow at the same rate.
x  g ( x )
1) If lim
x 
II) Indicate if the following grow faster, slower or at the same rate as ex.
a) x + 3
b)
x
 2
c) 3
x
d) ex/2
III) Indicate if the following grow faster, slower or at the same rate as x2.
a) x2 + 4x
b)
x 4  x3
c) 2x
d) log10 (x2)
IV) Indicate if the following grow faster, slower or at the same rate as ln x.
a) log3 x
b) ln x
c) 1/x
d) ex