- 11.3.1: Using Eulers method, complete the following table fory = (x 2)(y 3).
- 11.3.2: Using Eulers method, complete the following table fory = 4xy.
- 11.3.3: A population, P, in millions, is 1500 at time t = 0 andits growth i...
- 11.3.4: (a) Use Eulers method to approximate the value of yat x = 1 on the ...
- 11.3.5: (a) Use five steps of Eulers method to determine anapproximate solu...
- 11.3.6: (a) Use ten steps of Eulers method to determine anapproximate solut...
- 11.3.7: Consider the differential equation y = x + y whoseslope field is in...
- 11.3.8: (a) Using Figure 11.38, sketch the solution curve thatpasses throug...
- 11.3.9: Consider the solution of the differential equation y = ypassing thr...
- 11.3.10: Consider the differential equation y = (sin x)(sin y).(a) Calculate...
- 11.3.11: (a) Use Eulers method with five subintervals to approximatethe solu...
- 11.3.12: Why are the approximate results you obtained in smaller than the tr...
- 11.3.13: How do the errors of the five-step calculation and the tenstepcalcu...
- 11.3.14: (a) Use ten steps of Eulers method to approximate yvaluesfor dy/dt ...
- 11.3.15: Consider the differential equationdydx = 2x, with initial condition...
- 11.3.16: Consider the differential equationdydx = sin(xy), with initial cond...
- 11.3.17: Use Eulers method to estimate B(1), given thatdBdt = 0.05Band B = 1...
- 11.3.18: Consider the differential equation dy/dx = f(x) withinitial value y...
- 11.3.19: In 1920, explain what is wrong with the statement.Eulers method nev...
- 11.3.20: In 1920, explain what is wrong with the statement.If we use Eulers ...
- 11.3.21: In 2122, give an example ofA differential equation for which the ap...
- 11.3.22: In 2122, give an example ofA differential equation and initial cond...
- 11.3.23: Are the statements in 2324 true or false? Give anexplanation for yo...
- 11.3.24: Are the statements in 2324 true or false? Give anexplanation for yo...
Solutions for Chapter 11.3: EULERS METHOD
Full solutions for Calculus: Single and Multivariable | 6th Edition
The change in position divided by the change in time.
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
The function y = csc x
The function y = cot x
Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row
A variable that affects a response variable.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
See Linear regression line.
Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers
Negative linear correlation
See Linear correlation.
Order of magnitude (of n)
Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle
A matrix whose number of rows equals the number of columns.
The points x, y, 0 in Cartesian space.