MaTH 112: TEST 1 (A) - FALL 2025
Name: -
SHOW ALL YOUR WORK
1. Fill in the blanks (short answers).
for z in (-‘00 o0 )
i.) tan(tan"1(z)) = X
Z)(Orr
72X 0‘{ ) The domain of sin 1(33 ) is [‘ lj and the range is [_ %I .‘T/J
iii.) Some common properties of In are: ln (zy) = ’Q“' A '\“*‘Q-U‘j,
2 0.
3x° In(z/y) /&pfiw
= and In(z")= f‘*éa)(
P
0 \ iv.) Sincee® =expz = In~! z, it follows that e Inz _
2KV '
}.n em = K
a'nd,
\ T
and In, = & . More generally,
T v.) In terms of e -Qwa.
XK
2% 0
e
vi.) L’Hopital’s Rule is useful in findmg lim [ f(z)/g(x)], where both
XD QK L £6) and _ X @ %O\) are zero.
vii.) L'Hopital’s Rule says thitunder appropriate conditions,
lim £(2)/g(a) = lim /
viii.) If lim f(:z:) = 0 and hm g( ) = 00, then lim f(z)g(z) is an inde-
T—ra T—ra
OS terminate form. To apply L’Hé6pital’s Rule, we may rewrite
"e5)
this latter hmlt as /@Ab #C*)/
, ix.) Seven indeterminate forms are discussed in this book. They are
MR | o W _0
L/—xO.;J/ symbolized
by 0/0, co/00, 0-0c0 and R~ el l O
dx, we first rewrite it as Y(""‘ QV‘LX') Gm )‘-‘Dfix
03/ X-) Tb handle / cos®
7.y xi) f Oof(fv) dz is said to be %“Verj%'b if lim bf(:c)d:z:
exists and is finite.
a- - .
FP> \ |
\ ' , | xii.) /1 ;E]-;;dx converges if and only if
1 1 |
xiii.) The integral / —— dx does not exist in the proper sense because
Vz
0
0 .
the function f(z) = % is U»“LJOU»Y\&QJ on the interval
(0,1].
2. (a) Find the exact value of logg 27. == 3
(b) Solve for z:
& 4% = 16, = sz
Name: -
SHOW ALL YOUR WORK
1. Fill in the blanks (short answers).
for z in (-‘00 o0 )
i.) tan(tan"1(z)) = X
Z)(Orr
72X 0‘{ ) The domain of sin 1(33 ) is [‘ lj and the range is [_ %I .‘T/J
iii.) Some common properties of In are: ln (zy) = ’Q“' A '\“*‘Q-U‘j,
2 0.
3x° In(z/y) /&pfiw
= and In(z")= f‘*éa)(
P
0 \ iv.) Sincee® =expz = In~! z, it follows that e Inz _
2KV '
}.n em = K
a'nd,
\ T
and In, = & . More generally,
T v.) In terms of e -Qwa.
XK
2% 0
e
vi.) L’Hopital’s Rule is useful in findmg lim [ f(z)/g(x)], where both
XD QK L £6) and _ X @ %O\) are zero.
vii.) L'Hopital’s Rule says thitunder appropriate conditions,
lim £(2)/g(a) = lim /
viii.) If lim f(:z:) = 0 and hm g( ) = 00, then lim f(z)g(z) is an inde-
T—ra T—ra
OS terminate form. To apply L’Hé6pital’s Rule, we may rewrite
"e5)
this latter hmlt as /@Ab #C*)/
, ix.) Seven indeterminate forms are discussed in this book. They are
MR | o W _0
L/—xO.;J/ symbolized
by 0/0, co/00, 0-0c0 and R~ el l O
dx, we first rewrite it as Y(""‘ QV‘LX') Gm )‘-‘Dfix
03/ X-) Tb handle / cos®
7.y xi) f Oof(fv) dz is said to be %“Verj%'b if lim bf(:c)d:z:
exists and is finite.
a- - .
FP> \ |
\ ' , | xii.) /1 ;E]-;;dx converges if and only if
1 1 |
xiii.) The integral / —— dx does not exist in the proper sense because
Vz
0
0 .
the function f(z) = % is U»“LJOU»Y\&QJ on the interval
(0,1].
2. (a) Find the exact value of logg 27. == 3
(b) Solve for z:
& 4% = 16, = sz
