Homework Solutions

Solutions to homework in 2.1

#2 11

#6 100

#16 -4

#18 ¹/₁₀

#20 3x²

#22 3

#26 (a) -1
(b) 1
(c) DNE

#30 (a) DNE
(b) DNE
(c) DNE

#32 (a) 4
(b) 4
(c) 4
(d) 1
(e) 1
(f) 1

#34 (a) 1
(b) 2
(c) DNE
(d) -1
(e) -1
(f) -1

#36 (a) -1
(b) -2
(c) DNE
(d) 1
(e) 0
(f) DNE

#38 (a) DNE
(b) DNE
(c) DNE
(d) 0
(e) 0
(f) 0

#40 (a) 0
(b) DNE
(c) DNE
(d) 1
(e) 1
(f) 1

#44 (a) 0
(b) 0
(c) 0

#46 (a) -1
(b) -1
(c) -1

#56 Answers vary, but here's what you need to do: Use your calculator with f(x) = |x| and plug in values for x from both sides of 0 (such as x = -.1, -.01, -.001, .001, .01, .1) to support the claimed limit. The answer to the second question is "A calculator's data cannot be used to prove results on limits, though it can suggest that a certain limit exists."

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#2	11
#6	100
#16	-4
#18	¹/₁₀
#20	3x²
#22	3
#26	(a) -1 (b) 1 (c) DNE
#30	(a) DNE (b) DNE (c) DNE
#32	(a) 4 (b) 4 (c) 4 (d) 1 (e) 1 (f) 1
#34	(a) 1 (b) 2 (c) DNE (d) -1 (e) -1 (f) -1
#36	(a) -1 (b) -2 (c) DNE (d) 1 (e) 0 (f) DNE
#38	(a) DNE (b) DNE (c) DNE (d) 0 (e) 0 (f) 0
#40	(a) 0 (b) DNE (c) DNE (d) 1 (e) 1 (f) 1
#44	(a) 0 (b) 0 (c) 0
#46	(a) -1 (b) -1 (c) -1
#56	Answers vary, but here's what you need to do: Use your calculator with f(x) = \|x\| and plug in values for x from both sides of 0 (such as x = -.1, -.01, -.001, .001, .01, .1) to support the claimed limit. The answer to the second question is "A calculator's data cannot be used to prove results on limits, though it can suggest that a certain limit exists."