Review Problems for MATH185 Final Exam - Part A
Directions: Please submit this on Monday 11:59 PM.
1) Compute the following limit.
2) Compute the following limit.
3x2 x 2
x!1 5x3 + 4x + 1
lim
to
IE
lim
1
3
x!0
et
jim
fin
jfFy
3
ex
lim
lim
i
1
x2
x
o
x
so
0
y
and
we can use
n'hospital'srule
É
EEÉ
go
in
3) Compute the following limit.
4) Compute the following limit.
e2x 1
x!0 sin x
ln x
lim p
x!1
x
lim
lim
xo
him
sin
o
x
tis
1
3
O
o
I
e
2
2
O
1
and
5) Compute the following limit.
lim
x!3
x
x2
IT
IIIs
IT
I
6) Compute the following limit.
3
9
lim
x!⇡
tis
1 + cos x
1 cos x
2
I
I
116
7) Compute the following limit.
lim
x2
x!4
8) Compute the following limit.
2x 8
x 4
lim
x!0
II
IT
6
xx
ln (1 + x)
cos x + ex 1
1st
1
6
o
2
0
Fix
him
fixthft
9) Find the derivative of the function
f (x) = x2 5x + 1 using the limit definition.
10) Find the derivative of the function
f (x) = 2x 3 using the limit definition.
FIX th
Fix th
Fix
24
2
2
3
Fixthffex
lim
2
hoo
24
24
2
11) Findpthe derivative of the function
f (x) = x + 2 using the limit definition.
12) Find the derivative of the function
f (x) = x2 5x + 24 using the limit definition.
Similar
9
to
him
Iet
It
Extz
2x
3
5
3
21 4 3
2
24
2
3
2 X th
2
3
24
2
13) Find f 0 (x) if f (x) = x cos x.
Fix
14)Find f 0 (x) if
Xf sinx
x
f (x) =
cost
.
pxteygr.tt
sink t cost
fim
xsinxt
fix
se
Cota
16) Find f 0 (x) if f (x) = x3 tan x.
5
Fix
g
58ft
5
E fgthczt
4xtge
cost
15) Find f 0 (x) if f (x) = ln csc 5x.
f
2x + 1
2x + e4x
Cots
4
sect
x'faux
Ex
sinh
17) Find f 0 (x) if f (x) = x2 sin
rixexy.tw
IF
2
1
18)Find f 0 (x) if
(2x).
t2xsintkx
tax sin
sect 2 43 fan
4x Sec 12
2
.
ty
fan
YÉI ex
20) Find f 0 (x) if f (x) = ex cot x.
flexi etc
43 4x
43 tank
x2 + 5x 6
3e x + 5xx
tax
19) Find f 0 (x) if f (x) = sec (2x2 + 3).
Fix
f (x) =
3
5
csc
X t excotX
21) Find the slope of the curve at the given point
and write the equation of the tangent line in slope
intercept form.
22) Find the slope of the curve at the given point
and write the equation of the tangent line in slope
intercept form.
x4 + y 4 = 2; (1, 1)
y 2 = 4x; (1, 2)
4
2444
II
1
Y
C 17
D
11
X
Y
I
X
Ytl
Y
1
Y
24) Find the slope of the curve at the given point
and write the equation of the tangent line in slope
intercept form.
5; (1, ⇡)
cos y = x; (0,
x
Y
4
it
20
I
4
2
1
120417
6
⇡
)
2
1
sing 14
201
1
X
1
2
Z
23) Find the slope of the curve at the given point
and write the equation of the tangent line in slope
intercept form.
sin y = 5x4
it't.to
int
Y 1
11
y
Xt
It
0
25) Evaluate the indefinite integral
◆
Z ✓
1
x
sin x + 2 + 3e dx
x
26) Evaluate the indefinite integral
◆
p
Z ✓ 2
2x + 5 x 2
dx
x2
Ssinxixt Stax fse g
cost
t
te
t 38
g
text
I
cost
5
2
2
5
Y
3
J 4x
4x
t
413
dx
I
Gx
to
Etc
faux tin x
24
444.3
4
3
ok
28) Evaluate the indefinite integral
◆
Z ✓
1
2
2
sec x +
3x dx
x
t
4
2x
5
2x
27) Evaluate the indefinite integral
◆
Z ✓
p
4
3
4 x+ p
dx
3
x
six
t
c
7
x
te