Math 1432
*Bubble in PS ID very carefully – double/triple check!
*Bubble in Popper Number.
*Quiz in lab on Friday, Hw due in lab on Monday.
*My office hours at CASA: Fridays 11am – 2pm.
Popper#02
Question#
If 225 grams of a substance doubles in 8 days, what is the
growth factor (k)?
A)
225 / 8
B)
(ln 2) / 8
C)
(–ln 2) / 8
D)
(–ln 2) / 225
1
Question#
Give the domain of the function g  x   e
A) x > 0
B) x > – 5
C) x  – 5
D) x < – 5
x 5
.
E) none of the above
2
Inverse Trigonometric Functions
Section 7.7
3
Popper02
A
Q#
In the given right
triangle, AC =
x
B
1
C
2
A. x  1
B.
C.
2
x 1
2
x 1
2
D. x  1
E.
1 x
2
4
Quick review:
y = arcsin x find cos y
y  arc sec 5 find tan y
2
s i n  a r c s ec x  
5




cos 2 arcsin 3 
5
sin 2 arccos 4 
5
6
If
f (x) = y = arcsin x
then y’=
How about:
f (x) = y = arctan x
find y’
f (x) = y = arcsec x find y’
7
Formulas
d arcsi n x 


dx
1
1 x
2

d arctan x  1


2
dx
1 x
d arc sec x 


dx
1 x
2
 arcsi n x  C
dx  arct an x  C
 1  x2
1
x
dx
2
x 1

dx
2
x x 1
 arc sec x  C
8
Formulas (u is a function of x):
d  arcsinu  

dx 
u'

2
1u
d  arctanu   u'

2
dx 
1u
d  arc sec u  

dx 
u'
2
u u 1
du
2
2
a u
 arcsin u  C
a
du  1 arctan u  C
 a2  u2 a
a

du
2
2
u u a
u
1
 arc sec  C
a
a
9
Example: Give the domain of
derivative.
f  x   arctan  ln  x   and compute its
10
x
Example: Give the domain of g  x   arcsin e and find the equation for
2
the tangent line to the graph of this function at x = 0.
11
#12. Differentiate: y  tan
1
#16. Differentiate: f  x   e
x
tan 1 x
12
#20. Differentiate: y  sec
#40. Evaluate:
1
 1
1
2
x 2
dx
2
1 x
13
#42. Evaluate:
1
0
dx
4x
2
14
#46. Evaluate:
5
2
dx
2
9   x  2
15
Watch for details. These look similar.
1
 16  x2 dx
x
 16  x2 dx
Example:

x
1 x
4
dx
16
Popper02
Question#

du
2
2
a u

A. arcsin u  C
a
B. 1 arcsin u  C
a
a
C. 1 arctan u  C
a
a
D. arctan u  C
a
E. none of the above
17