- 9.5.1: Find particular solutions in 18. dy dt = 0.5(y 200), y= 50 when t = 0
- 9.5.2: Find particular solutions in 18. dP dt = P + 4, P = 100 when t = 0
- 9.5.3: Find particular solutions in 18. dH dt = 3(H 75), H= 0 when t = 0
- 9.5.4: Find particular solutions in 18. dm dt = 0.1m + 200, m(0) = 1000
- 9.5.5: Find particular solutions in 18. dB dt = 4B 100, B= 20 when t = 0
- 9.5.6: Find particular solutions in 18. dQ dt = 0.3Q 120, Q= 50 when t = 0
- 9.5.7: Find particular solutions in 18. dB dt + 2B = 50, B(1) = 100
- 9.5.8: Find particular solutions in 18. dB dt + 0.1B 10 = 0 B(2) = 3
- 9.5.9: Check that y = A+Cekt is a solution to the differential equation dy...
- 9.5.10: A bank account earns 5% annual interest, compounded continuously. M...
- 9.5.11: Money in an account earns interest at a continuous rate of 8% per y...
- 9.5.12: A company earns 2% per month on its assets, paid continuously, and ...
- 9.5.13: A bank account earns 7% annual interest compounded continuously. Yo...
- 9.5.14: One theory on the speed an employee learns a new task claims that t...
- 9.5.15: A patient is given the drug theophylline intravenously at a rate of...
- 9.5.16: A chain smoker smokes five cigarettes every hour. From each cigaret...
- 9.5.17: As you know, when a course ends, students start to forget the mater...
- 9.5.18: (a) Find the equilibrium solution of the equation dy dt = 0.5y 250....
- 9.5.19: (a) What are the equilibrium solutions for the differential equatio...
- 9.5.20: Figure 9.38 gives the slope field for a differential equation. Esti...
- 9.5.21: A yam is put in a 200C oven and heats up according to the different...
- 9.5.22: At 1:00 pm one winter afternoon, there is a power failure at your h...
- 9.5.23: A detective finds a murder victim at 9 am. The temperature of the b...
- 9.5.24: A drug is administered intravenously at a constant rate of r mg/hou...
- 9.5.25: Some people write the solution of the initial value problem dy dt =...
Solutions for Chapter 9.5: APPLICATIONS AND MODELING
Full solutions for Applied Calculus | 5th Edition
Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec
Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal
See Inverse cosecant function.
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
The change in position divided by the change in time.
Chord of a conic
A line segment with endpoints on the conic
Complements or complementary angles
Two angles of positive measure whose sum is 90°
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
See Power function.
Distance (on a number line)
The distance between real numbers a and b, or |a - b|
A visible representation of a numerical or algebraic model.
Integrable over [a, b] Lba
ƒ1x2 dx exists.
Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large
Multiplicative inverse of a matrix
See Inverse of a matrix
One-to-one rule of exponents
x = y if and only if bx = by.
Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.
See Power function
tan ?= sin ?cos ?and cot ?= cos ? sin ?
Sum of an infinite series
See Convergence of a series
Symmetric difference quotient of ƒ at a
ƒ(x + h) - ƒ(x - h) 2h