- 15.1.1: (a) Estimate the volume of the solid that lies below the surface an...
- 15.1.2: If , use a Riemann sum with , to estimate the value of . Take the s...
- 15.1.3: (a) Use a Riemann sum with to estimate the value of , where . Take ...
- 15.1.4: (a) Estimate the volume of the solid that lies below the surface an...
- 15.1.5: A table of values is given for a function defined on . (a) Estimate...
- 15.1.6: A 20-ft-by-30-ft swimming pool is filled with water. The depth is m...
- 15.1.7: Let be the volume of the solid that lies under the graph of and abo...
- 15.1.8: The figure shows level curves of a function in the square . Use the...
- 15.1.9: A contour map is shown for a function on the square . (a) Use the M...
- 15.1.10: The contour map shows the temperature, in degrees Fahrenheit, at 3:...
- 15.1.11: Evaluate the double integral by first identifying it as the volume ...
- 15.1.12: Evaluate the double integral by first identifying it as the volume ...
- 15.1.13: Evaluate the double integral by first identifying it as the volume ...
- 15.1.14: The integral , where , represents the volume of a solid. Sketch the...
- 15.1.15: Use a programmable calculator or computer (or the sum command on a ...
- 15.1.16: Repeat Exercise 15 for the integral .
- 15.1.17: If is a constant function, , and , show that
- 15.1.18: If , show that 0 xxR R 0, 1 0, 1 sinx y dA 1. xxR R
Solutions for Chapter 15.1: Double Integrals over Rectangles
Full solutions for Calculus, | 5th Edition
An interval that includes its endpoints
A letter or symbol that stands for a specific number,
Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists
Direction of an arrow
The angle the arrow makes with the positive x-axis
Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
Equivalent systems of equations
Systems of equations that have the same solution.
Focal length of a parabola
The directed distance from the vertex to the focus.
Frequency table (in statistics)
A table showing frequencies.
Side opposite the right angle in a right triangle.
Inverse tangent function
The function y = tan-1 x
The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole
A boxplot with the outliers removed.
Partial fraction decomposition
See Partial fractions.
Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22
Projection of u onto v
The vector projv u = au # vƒvƒb2v
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data
A set of points in Cartesian space equally distant from a fixed point called the center.
Trigonometric form of a complex number
r(cos ? + i sin ?)
Vector of length 1.