sheet19.pdf

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course Calculus
December7,2006
Problemsheet:del’HospitalRule
Findthelimits:
16.lim
x! 4
(tanx) tan2x
tanx−1
2sin 2 x−1
1
x − 1
17.lim
x!0
1.lim
x!0
e x −1
x
ln 1
x
2.lim
x!0
arcsin2x−2arcsinx
x 3
18.lim
x!0 +
1 x
1
p aarctan
r x
a −
p
r x
b
19.lim
x!1
tan x
2x+1
3.lim
x!0
x p x
barctan
1
!
ln(x+ p 1+x 2 ) − 1
a x −a sinx
x 3
20.lim
x!0
4.lim
x!0
ln(1+x)
a x −x a
x−a (a>0)
5.lim
x!1
x x −x
lnx−x+1
21.lim
x!a
(a+x) x −a x
x 2 (a>0)
x!1 − lnxln(1−x)
22.lim
x!0
2
arctanx
x
cos(sinx)−cosx
x 4
7.lim
x!0
23.lim
x!1
8.lim
x!0
1
x
1
tanhx − 1
24.lim
x!0
2
arccosx
1 x
tanx
x!0 + x x
x!1 (tanhx) x
x!0 x x x −1
26.lim
x!0
arcsinx
x
1 x 2
x!0 x x x −1
27.lim
x!0
sinx
x
1 x 2
x!0 + x k
1+lnx
1+e x
2
cothx
28.lim
x!0
x!1 x 1
1 − x
x lnx
(lnx) x
tanx
tana
cot(x−a)
29.lim
x!1
14.lim
x!a
x!1 (x+a) 1+ 1 x −x 1+ 1
30.) lim
x+a
x!1 (2−x) tan x 2
3 p
6.lim
25.lim
9.lim
10.lim
11.lim
12.lim
13.lim
15.lim
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