 1.1: Let be the function whose graph is given. (a) Estimate the value of...
 1.2: Determine whether each curve is the graph of a function of x. If it...
 1.3: If , evaluate the difference quotient
 1.4: Sketch a rough graph of the yield of a crop as a function of the am...
 1.5: Find the domain and range of the function. Write your answer in int...
 1.6: Find the domain and range of the function. Write your answer in int...
 1.7: Find the domain and range of the function. Write your answer in int...
 1.8: Find the domain and range of the function. Write your answer in int...
 1.9: . Suppose that the graph of is given. Describe how the graphs of th...
 1.10: The graph of is given. Draw the graphs of the following functions
 1.11: Use transformations to sketch the graph of the function.
 1.12: Use transformations to sketch the graph of the function.
 1.13: Use transformations to sketch the graph of the function.
 1.14: Use transformations to sketch the graph of the function.
 1.15: Use transformations to sketch the graph of the function.
 1.16: Use transformations to sketch the graph of the function.
 1.17: Determine whether is even, odd, or neither even nor odd.
 1.18: Find an expression for the function whose graph consists of the lin...
 1.19: If and , find the functions (a) , (b) , (c) , (d) , and their domains.
 1.20: Express the function as a composition of three functions
 1.21: Life expectancy improved dramatically in the 20th century. The tabl...
 1.22: A smallappliance manufacturer finds that it costs $9000 to produce...
 1.23: The graph of is given. (a) Find each limit, or explain why it does ...
 1.24: Sketch the graph of an example of a function that satisfies all of ...
 1.25: Find the limit.
 1.26: Find the limit.
 1.27: Find the limit.
 1.28: Find the limit.
 1.29: Find the limit.
 1.30: Find the limit.
 1.31: Find the limit.
 1.32: Find the limit.
 1.33: Find the limit.
 1.34: Find the limit.
 1.35: Find the limit.
 1.36: Find the limit.
 1.37: Find the limit.
 1.38: Find the limit.
 1.39: If for , find .
 1.41: Prove the statement using the precise definition of a limit.
 1.42: Prove the statement using the precise definition of a limit.
 1.43: Prove the statement using the precise definition of a limit.
 1.44: Prove the statement using the precise definition of a limit.
 1.45: Let (a) Evaluate each limit, if it exists. ( i) ( ii) ( iii) ( iv) ...
 1.46: . Let (a) For each of the numbers 2, 3, and 4, discover whether is ...
 1.47: Show that the function is continuous on its domain. State the domain
 1.48: Show that the function is continuous on its domain. State the domain
 1.49: Use the Intermediate Value Theorem to show that there is a root of ...
 1.50: Use the Intermediate Value Theorem to show that there is a root of ...
Solutions for Chapter 1: Single Variable Calculus 7th Edition
Full solutions for Single Variable Calculus  7th Edition
ISBN: 9780538497831
Solutions for Chapter 1
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus, edition: 7. Since 49 problems in chapter 1 have been answered, more than 4979 students have viewed full stepbystep solutions from this chapter. Single Variable Calculus was written by and is associated to the ISBN: 9780538497831. Chapter 1 includes 49 full stepbystep solutions.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Base
See Exponential function, Logarithmic function, nth power of a.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Commutative properties
a + b = b + a ab = ba

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

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.

Horizontal shrink or stretch
See Shrink, stretch.

Identity function
The function ƒ(x) = x.

Irrational zeros
Zeros of a function that are irrational numbers.

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Local extremum
A local maximum or a local minimum

Logistic regression
A procedure for fitting a logistic curve to a set of data

Multiplicative inverse of a matrix
See Inverse of a matrix

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Slopeintercept form (of a line)
y = mx + b

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.

Vertical component
See Component form of a vector.

Vertical line
x = a.