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Category > Calculus Posted 10 Jul 2017 My Price 9.00

Handout (Limits and Continuity)

Handout (Limits and Continuity)
(Schwartz; Math 157)
Work the problems on your own paper just like a normal homework assignment.
1. Sketch a possible graph of () given that lim+ () = 2, lim− () = 5, and (1) = 0.
→1 →1 ||; ≤ 2
and use it find each of the following limits. Then
√; > 2
check your answers by finding the limits numerically.
(a) lim− (()) 2. Sketch a graph of () = { →2 (b) lim+ (())
→2 (c) lim(())
→2 (d) lim (())
→−2 3. For each of the following, find the left- and right-hand limits at the given value of x then
determine whether the function is continuous at that value of x. For those that are not
continuous, state what the problem is in terms of limits.
+2
(a) () = |+2| at = 2.
+2 (b) () = |+2| at = −2.
2; ≤ 3
at = 3 + 9; > 3 2 +5 ; ≠ 0 (d) ℎ() = {
at = 0
0; = 0
(c) () = { 4. You should have found that () = { 2; ≤ 3
is not continuous at = 3. Pick a value + 9; > 3 2; ≤ 3
for C so that () = {
is continuous at = 3. + ; > 3 ; ≠ 0
2
5. You should have found that â„Ž() = { +5
is not continuous at = 0. However, you
0; = 0
could make it continuous if you define â„Ž(0) to be something other than zero. What would
â„Ž(0) have to be in order to make â„Ž() continuous?
2 − ; ≤ 3
6. Find values for m and n in the function () = {
so that lim () = 5. Then
− + ; > 3
→3
sketch the graph of ().

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SuperTutor
(15)
Status NEW Posted 10 Jul 2017 12:07 AM My Price 9.00

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