Stewart_Essential Calc_2e ch01sec01

MULTIPLE CHOICE

	1.	The graph of the function  is given. State the value of  .

a.		
b.		
c.		
d.		
e.		

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.1.3b
MSC:	Bimodal	NOT:	Section 1.1

	2.	The graphs of  and  are given. For what values of x is ?

a.	4, 2	
b.	0	
c.		
d.	–4, 12	
e.		

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.1.4b
MSC:	Bimodal	NOT:	Section 1.1

	3.	The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

a.	54	
b.	38	
c.		
d.	20	
e.	35	

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.1.9
MSC:	Bimodal	NOT:	Section 1.1

	4.	If , find and simplify , where .

a.		
b.		
c.		
d.		

ANS:	C	PTS:	1	DIF:	Easy	REF:	1.1.21
MSC:	Bimodal	NOT:	Section 1.1

	5.	If , evaluate the difference quotient .

a.		
b.		
c.		
d.	h	
e.	none of these	

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.1.22
MSC:	Bimodal	NOT:	Section 1.1

	6.	Find the domain of the function.

a.	(–, 0)
	
b.	
	
c.	
	
d.	(–, 0)  (0, )	

ANS:	D	PTS:	1	DIF:	Easy	REF:	1.1.25
MSC:	Bimodal	NOT:	Section 1.1

	7.	Find the domain and sketch the graph of the function. What is its range?

f (x) = 

a.	D: (–, ); R: [–1, ) 

	c.	D: (–, ); R: (–, 3]
	
b.	D: (–, ); R: (–, 0]  (3, )
	d.	D: (–, ); R: [0, ) 

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.1.39
MSC:	Bimodal	NOT:	Section 1.1

	8.	Find an expression for the function  whose graph is the bottom half of the parabola 
.

a.		
b.		
c.		
d.		
e.		

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.1.45
MSC:	Bimodal	NOT:	Section 1.1

	9.	A rectangle has perimeter  m. Express the area of the rectangle as a function  of the length  of one of its sides.

a.		
b.		
c.		
d.		
e.		

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.1.47
MSC:	Bimodal	NOT:	Section 1.1

	10.	An open rectangular box with volume   has a square base. Express the surface area of the box as a function  of the length  of a side of the base.

a.	
	
b.	
	
c.	
	
d.	
	
e.		

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.1.51
MSC:	Bimodal	NOT:	Section 1.1

	11.	Determine whether the function whose graph is given  is even, odd, or neither. 

a.	Even	
b.	Neither	
c.	Odd	

ANS:	A	PTS:	1	DIF:	Medium	REF:	1.1.55
MSC:	Bimodal	NOT:	Section 1.1

	12.	If the point  is on the graph of an even function, what other point must also be on the graph? 

a.		
b.		
c.		
d.		
e.	None of these	

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.1.57a
MSC:	Bimodal	NOT:	Section 1.1

	13.	Which of the following graphs is neither even nor odd? 

a.		
b.		
c.		

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.1.60
MSC:	Bimodal	NOT:	Section 1.1

NUMERIC RESPONSE

	1.	The graphs of  and  are given.
Find the values of  and .

ANS:	, 

PTS:	1	DIF:	Medium	REF:	1.1.4a	
MSC:	Numerical Response		NOT:	Section 1.1

	2.	Find the domain of the function.

ANS:	

PTS:	1	DIF:	Medium	REF:	1.1.26	
MSC:	Numerical Response		NOT:	Section 1.1

	3.	Find the domain of the function.

ANS:	

PTS:	1	DIF:	Medium	REF:	1.1.27	
MSC:	Numerical Response		NOT:	Section 1.1

	4.	Determine whether  f  is even, odd, or neither.

ANS:	even

PTS:	1	DIF:	Medium	REF:	1.1.56	
MSC:	Numerical Response		NOT:	Section 1.1

SHORT ANSWER

	1.	Refer to the graph of the function  f  in the following figure.

a. Find f (1).
b. Find the value of x for which (i)  and (ii) .
c. Find the domain and range of f.

ANS:	
a. 0
b. (i) 2 (ii) 1, 3
c. D: [1, 4], R: [–3, 1]

PTS:	1	DIF:	Easy	REF:	1.1.3a	MSC:	Short Answer
NOT:	Section 1.1

	2.	If f (x) = 

find f (–4), f (0), and f (1).

ANS:	
f (–4) = 19, f (0) = 3, f (1) = 1.

PTS:	1	DIF:	Easy	REF:	1.1.19	MSC:	Short Answer
NOT:	Section 1.1

	3.	Determine whether the function is even, odd, or neither.

ANS:	
Odd

PTS:	1	DIF:	Medium	REF:	1.1.63	MSC:	Short Answer
NOT:	Section 1.1

Stewart_Essential Calc_2e ch01sec02

MULTIPLE CHOICE

	1.	The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

What is the F-intercept and what does it represent? 

a.	, Fahrenheit temperature corresponding to 
	
b.	32, Fahrenheit temperature corresponding to 
	
c.	32, Celsius temperature corresponding to 
	
d.	0, Fahrenheit temperature corresponding to 
	
e.	, Celsius temperature corresponding to 	

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.2.9b
MSC:	Bimodal	NOT:	Section 1.2

	2.	The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her  to drive  mi and in July it cost her  to drive  mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model. 

a.		
b.		
c.		
d.		
e.		

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.2.14a
MSC:	Bimodal	NOT:	Section 1.2

	3.	Many physical quantities are connected by inverse square laws, that is, by power functions of the form 
                . 
In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move 
                 
the distance to the lamp. How much brighter is the light?

a.	 times
	
b.	 times
	
c.	 times
	
d.	 times
	
e.	 times

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.2.15
MSC:	Bimodal	NOT:	Section 1.2

NUMERIC RESPONSE

	1.	The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

Complete the table and find the slope.

		

ANS:	; slope = 

PTS:	1	DIF:	Medium	REF:	1.2.9a	
MSC:	Numerical Response		NOT:	Section 1.2

	2.	It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in  of the caves by the equation 

(a) The cave called mission impossible near puebla, mexico, has surface area of .    
      How many species of bats would expect to find in that cave?

(b) If you discover that  species of bats live in cave estimate the area of the cave.

ANS:	
a)  species
b) 

PTS:	1	DIF:	Medium	REF:	1.2.16	
MSC:	Numerical Response		NOT:	Section 1.2

Stewart_Essential Calc_2e ch01sec03

MULTIPLE CHOICE

	1.	Use the graph of the function to state the value of , if it exists.

a.	
	
b.	
	
c.	
	
d.	
	
e.	does not exist	

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.3.15
MSC:	Bimodal	NOT:	Section 1.3

	2.	Use the graph of the function to state the value of  if it exists. 

a.	
	
b.	1
	
c.	
	
d.	
	
e.	does not exist	

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.3.18
MSC:	Bimodal	NOT:	Section 1.3

	3.	Estimate the value of the following limit by graphing the function .  

Round your answer correct to two decimal places. 

a.	3.18	
b.		
c.		
d.		
e.		

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.3.20a
MSC:	Bimodal	NOT:	Section 1.3

NUMERIC RESPONSE

	1.	By graphing the function 

and zooming in toward the point where the graph crosses the y-axis, estimate the value of 

ANS:	

PTS:	1	DIF:	Medium	REF:	1.3.19a	
MSC:	Numerical Response		NOT:	Section 1.3

	2.	Evaluate the function

at the given numbers (correct to six decimal places). Use the results to guess the value of the limit 

ANS:	

PTS:	1	DIF:	Medium	REF:	1.3.21a	
MSC:	Numerical Response		NOT:	Section 1.3

SHORT ANSWER

	1.	Complete the table by computing  at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

x							

ANS:	

x							
	–0.34483	–0.33445	–0.33344	–0.33322	–0.33223	–0.32258	

–0.333

PTS:	1	DIF:	Medium	REF:	1.3.11	MSC:	Short Answer
NOT:	Section 1.3

	2.	Complete the table by computing  at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

x	4.9	4.99	4.999	5.001	5.01	5.1	

ANS:	

x	4.9	4.99	4.999	5.001	5.01	5.1	
	0.1001	0.10001	0.1	0.1	0.09999	0.0999	

0.1

PTS:	1	DIF:	Medium	REF:	1.3.12	MSC:	Short Answer
NOT:	Section 1.3

	3.	Complete the table by computing  at the given values of x, accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places.

							

ANS:	

	0.20858	0.20008	0.2	0.2	0.20008	0.20858	

0.2

PTS:	1	DIF:	Medium	REF:	1.3.13	MSC:	Short Answer
NOT:	Section 1.3

Stewart_Essential Calc_2e ch01sec04

MULTIPLE CHOICE

	1.	Find the limit .

a.	12	
b.	–12	
c.	6	
d.	–1	

ANS:	A	PTS:	1	DIF:	Easy	REF:	1.4.3
MSC:	Bimodal	NOT:	Section 1.4

	2.	Evaluate the limit.

a.		
b.		
c.		
d.		
e.		

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.4.4
MSC:	Bimodal	NOT:	Section 1.4

	3.	Find the limit. 

a.		
b.		
c.		
d.		
e.		

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.4.11
MSC:	Bimodal	NOT:	Section 1.4

	4.	Find the limit , if it exists.

a.	2	
b.	5	
c.	3	
d.	Does not exist	

ANS:	B	PTS:	1	DIF:	Medium	REF:	1.4.13
MSC:	Bimodal	NOT:	Section 1.4

	5.	Find the limit .

a.	
	
b.	
	
c.	
	
d.	1	

ANS:	B	PTS:	1	DIF:	Easy	REF:	1.4.14
MSC:	Bimodal	NOT:	Section 1.4

	6.	Evaluate the limit, if it exists. 

a.		
b.	1	
c.		
d.		
e.	does not exist	

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.4.17
MSC:	Bimodal	NOT:	Section 1.4

	7.	Find the limit , if it exists.

a.	
	
b.	
	
c.	
	
d.	Does not exist	

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.4.21
MSC:	Bimodal	NOT:	Section 1.4

NUMERIC RESPONSE

	1.	Find the limit. 

ANS:	

PTS:	1	DIF:	Medium	REF:	1.4.5	
MSC:	Numerical Response		NOT:	Section 1.4

	2.	Evaluate the limit. 

ANS:	

PTS:	1	DIF:	Medium	REF:	1.4.19	
MSC:	Numerical Response		NOT:	Section 1.4

	3.	Evaluate the limit. 

ANS:	0

PTS:	1	DIF:	Medium	REF:	1.4.37	
MSC:	Numerical Response		NOT:	Section 1.4

SHORT ANSWER

	1.	Find the limit , if it exists.

ANS:	

PTS:	1	DIF:	Medium	REF:	1.4.12	MSC:	Short Answer
NOT:	Section 1.4

	2.	Find the limit .

ANS:	

PTS:	1	DIF:	Easy	REF:	1.4.23	MSC:	Short Answer
NOT:	Section 1.4

Stewart_Essential Calc_2e ch01sec05

MULTIPLE CHOICE

	1.	Choose an equation from the following that expresses the fact that a function  f  is continuous at the number . 

a.	
	
b.	
	
c.	
	
d.	
	
e.		

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.5.1
MSC:	Bimodal	NOT:	Section 1.5

	2.	If f and g are continuous functions with 

a.		
b.		
c.		
d.		
e.		

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.5.11
MSC:	Bimodal	NOT:	Section 1.5

	3.	Use continuity to evaluate the limit. 

a.		
b.	1	
c.	0	
d.		
e.		

ANS:	C	PTS:	1	DIF:	Medium	REF:	1.5.28
MSC:	Bimodal	NOT:	Section 1.5

	4.	Determine where f  is discontinuous.

a.	0 only	
b.		
c.	 only	
d.		
e.	 only	

ANS:	D	PTS:	1	DIF:	Medium	REF:	1.5.31
MSC:	Bimodal	NOT:	Section 1.5

	5.	For what value of the constant c is the function  f  continuous on 

a.		
b.		
c.		
d.		
e.		

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.5.33
MSC:	Bimodal	NOT:	Section 1.5

NUMERIC RESPONSE

	1.	For  determine whether  f  is continuous from the right, from the left, or neither. 

ANS:	neither

PTS:	1	DIF:	Medium	REF:	1.5.3b	
MSC:	Numerical Response		NOT:	Section 1.5

	2.	Determine where f  is discontinuous.

ANS:	

PTS:	1	DIF:	Medium	REF:	1.5.16	
MSC:	Numerical Response		NOT:	Section 1.5

Stewart_Essential Calc_2e ch01sec06

MULTIPLE CHOICE

	1.	Let  Find the following limits. 

a.	 and 	
b.	both 	
c.	both 1	
d.	 and 	
e.	 and 	

ANS:	A	PTS:	1	DIF:	Medium	REF:	1.6.13
MSC:	Bimodal	NOT:	Section 1.6

	2.	Find the limit.

a.		
b.		
c.		
d.		
e.		

ANS:	D	PTS:	1	DIF:	Easy	REF:	1.6.19
MSC:	Bimodal	NOT:	Section 1.6

	3.	Find the limit.

a.		
b.		
c.		
d.		
e.		

ANS:	D	PTS:	1	DIF:	Easy	REF:	1.6.32
MSC:	Bimodal	NOT:	Section 1.6

	4.	Find the vertical asymptotes of the function.

a.	
	
b.	
	
c.	
	
d.	
	
e.	None of these	

ANS:	E	PTS:	1	DIF:	Medium	REF:	1.6.35
MSC:	Bimodal	NOT:	Section 1.6

NUMERIC RESPONSE

	1.	For the function f whose graph is shown, state the following. 

ANS:	

PTS:	1	DIF:	Medium	REF:	1.6.1d	
MSC:	Numerical Response		NOT:	Section 1.6