- 5.1: Suppose that f (x) = xex , x 0 (a) Show that f (0) = 0, f (x) > 0 f...
- 5.2: Suppose that f (x) = x ln x, x > 0 (a) Define f (x) at x = 0 so tha...
- 5.3: In Review of Chapter 2 we introduced the hyperbolic functions sinh ...
- 5.4: Let f (x) = x 1 + ex , x R (a) Show that y = 0 is a horizontal asym...
- 5.5: Recruitment Model Rickers curve describes the relationship between ...
- 5.6: Gompertz Growth Model The is sometimes used to study the growth of ...
- 5.7: Monod Growth Model The Monod growth curve is given by f (x) = cx k ...
- 5.8: Logistic Growth The logistic growth curve is given by N(t) = K 1 + ...
- 5.9: Genetics A population is said to be in HardyWeinberg equilibrium, w...
- 5.10: Cell Volume Suppose the volume of a cell is increasing at a constan...
- 5.11: Drug Concentration Suppose the concentration c(t) of a drug in the ...
- 5.12: Resource-Limited Growth Sterner (1997) investigated the effect of f...
- 5.13: Velocity and Distance Neglecting air resistance, the height (in met...
Solutions for Chapter 5: Review Problems
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series) | 3rd Edition
Annual percentage yield (APY)
The rate that would give the same return if interest were computed just once a year
Trigonometric functions when applied to real numbers are circular functions
An event whose probability depends on another event already occurring
equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)
Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).
Variable representing the domain value of a function (usually x).
Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).
Notation used to specify intervals, pp. 4, 5.
Inverse cosecant function
The function y = csc-1 x
Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c
Newton’s law of cooling
T1t2 = Tm + 1T0 - Tm2e-kt
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.
See Polar coordinate system.
A degree 4 polynomial function.
Zeros of multiplicity ? 2 (see Multiplicity).
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
Vertex of a cone
See Right circular cone.
Vertical line test
A test for determining whether a graph is a function.
The x-value of the left side of the viewing window,.
The scale of the tick marks on the y-axis in a viewing window.