 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 u...
 15.1.6: A 20ftby30ft 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 4:...
 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: Use the result of Exercise 17 to show that where .
Solutions for Chapter 15.1: DOUBLE INTEGRALS OVER RECTANGLES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 15.1: DOUBLE INTEGRALS OVER RECTANGLES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Chapter 15.1: DOUBLE INTEGRALS OVER RECTANGLES includes 18 full stepbystep solutions. Since 18 problems in chapter 15.1: DOUBLE INTEGRALS OVER RECTANGLES have been answered, more than 21950 students have viewed full stepbystep solutions from this chapter. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Factored form
The left side of u(v + w) = uv + uw.

Focal length of a parabola
The directed distance from the vertex to the focus.

Future value of an annuity
The net amount of money returned from an annuity.

Horizontal translation
A shift of a graph to the left or right.

Interval
Connected subset of the real number line with at least two points, p. 4.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Linear regression equation
Equation of a linear regression line

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Pointslope form (of a line)
y  y1 = m1x  x 12.

Positive linear correlation
See Linear correlation.

Principle of mathematical induction
A principle related to mathematical induction.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Rose curve
A graph of a polar equation or r = a cos nu.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Unit vector
Vector of length 1.