- 2.1.1: A tank holds 1000 gallons of water, which drains from the bottom of...
- 2.1.2: A cardiac monitor is used to measure the heart rate of a patient af...
- 2.1.3: The point lies on the curve . (a) If is the point , use your calcul...
- 2.1.4: The point lies on the curve . (a) If is the point , use your calcul...
- 2.1.5: . If a ball is thrown into the air with a velocity of 40 fts, its h...
- 2.1.6: If a rock is thrown upward on the planet Mars with a velocity of 10...
- 2.1.7: The table shows the position of a cyclist. (a) Find the average vel...
- 2.1.8: The displacement (in centimeters) of a particle moving back and for...
- 2.1.9: The point lies on the curve . (a) If is the point , find the slope ...
- 2.1.46: . In the theory of relativity, the mass of a particle with velocity...
- 2.1.47: Use a graph to estimate the equations of all the vertical asymptote...
- 2.1.48: (a) Use numerical and graphical evidence to guess the value of the ...
Solutions for Chapter 2.1: The Tangent and Velocity Problems
Full solutions for Calculus: Early Transcendentals | 7th Edition
Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.
A polynomial with exactly two terms
Combinations of n objects taken r at a time
There are nCr = n! r!1n - r2! such combinations,
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.
General form (of a line)
Ax + By + C = 0, where A and B are not both zero.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
The difference between the third quartile and the first quartile.
Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial
Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)
Multiplicative identity for matrices
See Identity matrix
A logarithm with base e.
See Additive inverse of a real number and Additive inverse of a complex number.
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.
Zeros of multiplicity ? 2 (see Multiplicity).
A number that measures a quantitative variable for a sample from a population.
Sum of an infinite series
See Convergence of a series
A line graph in which time is measured on the horizontal axis.