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Activity 4.6a Indeterminate Forms and L'Hopital's Rule
Instructions: For each of the following limits, determine which indeterminate form the
function gives at the specified point and whether or not you can use l'Hopital's rule. If the
answer is yes, use I'Hopital's to evaluate the given limit. If the answer is no, use another
method to evaluate the limit. If you use I'Hopital's, state when you use it.
1.
lim x1/(lx)
x+l+
o/{)
I
I
vn
J1Vt1
:x
JAVv1
~~ ,

;:::

J
.k
'l'f
)\7J +
X''') I
JIV}")
VI7
I
I
..
~
)~
A :::
:=
Z
x; \t
  
lim (In x) l/x
x+oo
\ ".,
(.JY 00
0
')
'... ,
  __ ... ___ . _______ 0'" .
2.
JuY' In [{1M "f)YX J
rf~(/Q
pm
~(kv?C)
/("')(0 )C
f. M
\
vOl

'
~
~':(VI
ftx
x

~VV1 ~
7f.~:X
'Ie "/0
)(")0
:= 0.
lim (In x) l/(xe)
x+e+
3.
~ [()v, X '{t<e)l : ~Wl ...
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