5128_Ch03_pp098-184
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Review Exercises 181<br />
Calculus at Work<br />
Iwork at Ramsey County Hospital and<br />
other community hospitals in the Minneapolis<br />
area, both with patients and in<br />
a laboratory. I have wanted to be a physician<br />
since I was about 12 years old, and I<br />
began attending medical school when I<br />
was 30 years old. I am now working in the<br />
field of internal medicine.<br />
Cardiac patients are common in my<br />
field, especially in the diagnostic stages.<br />
One of the machines that is sometimes<br />
used in the emergency room to diagnose<br />
problems is called a Swan-Ganz catheter,<br />
named after its inventors Harold James<br />
Swan and William Ganz. The catheter is inserted<br />
into the pulmonary artery and then<br />
is hooked up to a cardiac monitor. A program<br />
measures cardiac output by looking<br />
at changes of slope in the curve. This information<br />
alerts me to left-sided heart<br />
failure.<br />
Lupe Bolding, M.D.<br />
Ramsey County Hospital<br />
Minneapolis, MN<br />
Chapter 3 Key Terms<br />
acceleration (p. 130)<br />
average velocity (p. 128)<br />
Chain Rule (p. 149)<br />
Constant Multiple Rule (p. 117)<br />
Derivative of a Constant Function (p. 116)<br />
derivative of f at a (p. 99)<br />
differentiable function (p. 99)<br />
differentiable on a closed interval (p. 104)<br />
displacement (p. 128)<br />
free-fall constants (p. 130)<br />
implicit differentiation (p. 157)<br />
instantaneous rate of change (p. 127)<br />
instantaneous velocity (p. 128)<br />
Intermediate Value Theorem for<br />
Derivatives (p. 113)<br />
1 1<br />
7. <br />
2x 2x<br />
3/2<br />
Chapter 3 Review Exercises<br />
inverse function–inverse cofunction<br />
identities (p. 168)<br />
jerk (p. 144)<br />
left-hand derivative (p. 104)<br />
local linearity (p. 110)<br />
logarithmic differentiation (p. 177)<br />
marginal cost (p. 134)<br />
marginal revenue (p. 134)<br />
nth derivative (p. 122)<br />
normal to the surface (p. 159)<br />
numerical derivative NDER (p. 111)<br />
orthogonal curves (p. 154)<br />
orthogonal families (p. 180)<br />
Power Chain Rule (p. 151)<br />
Power Rule for Arbitrary Real Powers (p. 176)<br />
1<br />
17. cos 1 <br />
x1x <br />
2<br />
Power Rule for Negative Integer<br />
Powers of x (p. 121)<br />
Power Rule for Positive Integer<br />
Powers of x (p. 116)<br />
Power Rule for Rational Powers<br />
of x (p. 161)<br />
Product Rule (p. 119)<br />
Quotient Rule (p. 120)<br />
right-hand derivative (p. 104)<br />
sensitivity to change (p. 133)<br />
simple harmonic motion (p. 143)<br />
speed (p. 129)<br />
Sum and Difference Rule (p. 117)<br />
symmetric difference quotient (p. 111)<br />
velocity (p. 128)<br />
2<br />
18. <br />
l n2<br />
The collection of exercises marked in red could be used as a chapter<br />
test.<br />
In Exercises 1–30, find the derivative of the function.<br />
5x 2 csc 5x cot 5x 2x csc 5x<br />
1<br />
11. y x 2 csc 5x 12. y ln x , x 0 2<br />
13. y ln 1 e x e<br />
x x<br />
14. y xe x 1 e x<br />
xe x e x<br />
15. y e 1ln x e 16. y ln sin x<br />
1. y x 5 1 17. r ln cos 1 x 18. r log 2 u 2 <br />
8 x2 1 4 x 2. y 3 7x3 3x 7 21x 2 21x 6<br />
5x 4 x 1<br />
4 4 19. s log 5 t 7 20. s 8 t 8 t ln 8<br />
3. y 2 sin x cos x 4. y 2 x 1<br />
1<br />
4<br />
, t 7<br />
<br />
2x<br />
1<br />
21. y x ln x 2x2 See page <strong>184</strong>. 22. y <br />
x (2x 1) 2<br />
(t 7)ln 5<br />
2 cos 2 x 2 sin 2 x 2 cos 2x<br />
x 2 1<br />
5. s cos 1 2t 2 sin (1 – 2t) 6. s cot 2 23. y e tan1 x e<br />
t an1x<br />
t 2<br />
t2 csc2 2 See page <strong>184</strong>.<br />
t <br />
24. y sin 1 1 u 2 <br />
1 x2<br />
1<br />
3x 1<br />
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<br />
x<br />
2x See<br />
1<br />
page <strong>184</strong>.<br />
See page <strong>184</strong>.<br />
9. r sec 1 3u 10. r tan 2 3 u 2 <br />
27. y z cos 1 z 1 z 2 28. y 2x 1 csc 1 x<br />
3 sec (1 3) tan (1 3) 4 tan (3 2 ) sec 2 (3 2 )<br />
cos 1 z<br />
1 x c sc 1x<br />
<br />
1<br />
x <br />
16. cot x, where x is an interval of the form (k, (k 1) ), k even