5128_Ch03_pp098-184

Review Exercises 181
Calculus at Work
Iwork at Ramsey County Hospital and
other community hospitals in the Minneapolis
area, both with patients and in
a laboratory. I have wanted to be a physician
since I was about 12 years old, and I
began attending medical school when I
was 30 years old. I am now working in the
field of internal medicine.
Cardiac patients are common in my
field, especially in the diagnostic stages.
One of the machines that is sometimes
used in the emergency room to diagnose
problems is called a Swan-Ganz catheter,
named after its inventors Harold James
Swan and William Ganz. The catheter is inserted
into the pulmonary artery and then
is hooked up to a cardiac monitor. A program
measures cardiac output by looking
at changes of slope in the curve. This information
alerts me to left-sided heart
failure.
Lupe Bolding, M.D.
Ramsey County Hospital
Minneapolis, MN
Chapter 3 Key Terms
acceleration (p. 130)
average velocity (p. 128)
Chain Rule (p. 149)
Constant Multiple Rule (p. 117)
Derivative of a Constant Function (p. 116)
derivative of f at a (p. 99)
differentiable function (p. 99)
differentiable on a closed interval (p. 104)
displacement (p. 128)
free-fall constants (p. 130)
implicit differentiation (p. 157)
instantaneous rate of change (p. 127)
instantaneous velocity (p. 128)
Intermediate Value Theorem for
Derivatives (p. 113)
1 1
7.
2x 2x
3/2
Chapter 3 Review Exercises
inverse function–inverse cofunction
identities (p. 168)
jerk (p. 144)
left-hand derivative (p. 104)
local linearity (p. 110)
logarithmic differentiation (p. 177)
marginal cost (p. 134)
marginal revenue (p. 134)
nth derivative (p. 122)
normal to the surface (p. 159)
numerical derivative NDER (p. 111)
orthogonal curves (p. 154)
orthogonal families (p. 180)
Power Chain Rule (p. 151)
Power Rule for Arbitrary Real Powers (p. 176)
1
17. cos 1
x1x
2
Power Rule for Negative Integer
Powers of x (p. 121)
Power Rule for Positive Integer
Powers of x (p. 116)
Power Rule for Rational Powers
of x (p. 161)
Product Rule (p. 119)
Quotient Rule (p. 120)
right-hand derivative (p. 104)
sensitivity to change (p. 133)
simple harmonic motion (p. 143)
speed (p. 129)
Sum and Difference Rule (p. 117)
symmetric difference quotient (p. 111)
velocity (p. 128)
2
18.
l n2
The collection of exercises marked in red could be used as a chapter
test.
In Exercises 1–30, find the derivative of the function.
5x 2 csc 5x cot 5x 2x csc 5x
1
11. y x 2 csc 5x 12. y ln x , x 0 2
13. y ln 1 e x e
x x
14. y xe x 1 e x
xe x e x
15. y e 1ln x e 16. y ln sin x
1. y x 5 1 17. r ln cos 1 x 18. r log 2 u 2
8 x2 1 4 x 2. y 3 7x3 3x 7 21x 2 21x 6
5x 4 x 1
4 4 19. s log 5 t 7 20. s 8 t 8 t ln 8
3. y 2 sin x cos x 4. y 2 x 1
1
4
, t 7
2x
1
21. y x ln x 2x2 See page 184. 22. y
x (2x 1) 2
(t 7)ln 5
2 cos 2 x 2 sin 2 x 2 cos 2x
x 2 1
5. s cos 1 2t 2 sin (1 – 2t) 6. s cot 2 23. y e tan1 x e
t an1x
t 2
t2 csc2 2 See page 184.
t
24. y sin 1 1 u 2
1 x2
1
3x 1
7. y x 1 8. y x2x 1 25. y t sec 1 t 1 2 ln t 26. y 1 t 2 cot 1 2t
x
2x See
1
page 184.
See page 184.
9. r sec 1 3u 10. r tan 2 3 u 2
27. y z cos 1 z 1 z 2 28. y 2x 1 csc 1 x
3 sec (1 3) tan (1 3) 4 tan (3 2 ) sec 2 (3 2 )
cos 1 z
1 x c sc 1x
1
x
16. cot x, where x is an interval of the form (k, (k 1) ), k even