REVIEW I

1. Find the limits

a)
b)
c)
d)
e)

2. Find the limits of the following sequences

a)
b)

3. Using the Squeeze Principle find the limits
:

a)
b)
c)
d)

e)

4. Find the limits of the following sequences:

and
,

and then using the Squeeze Principle find the limit of z_n
:

.

5. Find the limits
(Hint: the `e' limit)

a)
b)
c)
d)

e)
f)
g)

h)
i)

6. Use the Bounded Monotone Sequence Theorem to find the limit
for

a )
b)
c)
d)

7. Test for convergence or divergence
, for a_n given by:

a)
(necessary cond.) b)
(Ratio T.) c)
(Root T.)

d)
(necessary cond.)

e)
(compare with
)

f)
(compare with
)

8. Determine convergence or divergence of the following series (Root or Ratio Test)

a)

; b)
c)

d)
.

9*. Formulate the Comparison Convergence Test and use it to test convergence or divergence of the series

10. Formulate the Alternating Series Test and use it to determine convergence or divergence of the series

.

11. Determine the type of convergence (absolute or conditional) of the series:

.

12. Find the following limits

a)
b)
c)

“e limit”: d)
e)
f)

“six/x limit“: g)
h)
i)

13. Determine whether the following functions are continuous

a)
b)

14. Find the values of parameters 'a' and `b' such that the function

is continuous R

15. Find the values of the parameters 'a' and `b' for which the function

is continuous in the interval
.

16. Determine such values of the parameters 'a' and `b' that the function

is continuous in R.

17. Determine the values of the parameters `a' and `b' for which the function

is continuous in

18. Show that the following limit does not exist:

a)
b)
c)
d)

19*. Show that
has at least one root in the interval

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