MATH 112: TesT 1 (B) : | | FALL 2025
Name:
SHOW ALL YOUR WORK
" 1. Fill in the blanks (short answers).
i.) tan~(tan(z)) - >< \.fora‘cin C T/ WZ_\
2’(0\&“
9x0.0 [ ii.) 1) The domain of cos (z)is__|_ £ and the range is E 0 (’\{
iii.) Some common properties of In are: In(zy) ¢Q4X + ’Qt\:{ ,
3’(08/ | l¥1(m/y)= ‘e\,X"’ «Qk‘({) _and ln(:g:’)*—- f\véa)\
iv.) Two remarkable facts about e® are that ac-i—z(e‘") =_
0 X
K and,/e“’dm——:: € ‘f*C. .
- V.) In terms of e and In, V3 =
- ‘e.
B| .
___. More generally,
- X v B - |
vi.) L’Hop1ta.1’s Rule is useful in findmg l1m [ f (z)/ g(a:)] Where both
%05 e )and /L-:jq %OL) are zero.
vil.
) L’Hop1ta,1’s Rule says tha,t under appropriate condltlons
.‘ S\ o limf(:r;)/g(:n)= %)%/
lim
r—a
v111) If hm f(:c) =0 and. lin g(:c) 00, then lim f (z)g(z) is an mde-
O S- | termma,te form To a,pply L’Hoépital’s Rule, we may rewrite
this latter limit a8
, ix.) Seven indeterminate forms are dlscussed in this book They are
, o
symbohzedbyO/O oo/oo 0- ooa.nd’oo“‘"o O ‘ { ‘_OO
%(OJ—
O 5_ - x.) Tohandle / cos® z di, we first rewrite it as _
- F
o0
@ r xi.) / - cosx dz does not converge because QLM%WB"" S&N- Q=
does not exist. b o4
/o fcm X
(' xn)/ a—--dmconvergesfiandonlylf ' m bflOO *
| 1 _
xiii.) The integral —— dx does not exist in the proper sense
DS¢ because the function o1
f(z) = assumes arbitrarily large
values near the point Lf
2. (a) Find the exact value of log; 27. = 4
9
(b) Solve for z:
2 i | 63—593 =4,
Name:
SHOW ALL YOUR WORK
" 1. Fill in the blanks (short answers).
i.) tan~(tan(z)) - >< \.fora‘cin C T/ WZ_\
2’(0\&“
9x0.0 [ ii.) 1) The domain of cos (z)is__|_ £ and the range is E 0 (’\{
iii.) Some common properties of In are: In(zy) ¢Q4X + ’Qt\:{ ,
3’(08/ | l¥1(m/y)= ‘e\,X"’ «Qk‘({) _and ln(:g:’)*—- f\véa)\
iv.) Two remarkable facts about e® are that ac-i—z(e‘") =_
0 X
K and,/e“’dm——:: € ‘f*C. .
- V.) In terms of e and In, V3 =
- ‘e.
B| .
___. More generally,
- X v B - |
vi.) L’Hop1ta.1’s Rule is useful in findmg l1m [ f (z)/ g(a:)] Where both
%05 e )and /L-:jq %OL) are zero.
vil.
) L’Hop1ta,1’s Rule says tha,t under appropriate condltlons
.‘ S\ o limf(:r;)/g(:n)= %)%/
lim
r—a
v111) If hm f(:c) =0 and. lin g(:c) 00, then lim f (z)g(z) is an mde-
O S- | termma,te form To a,pply L’Hoépital’s Rule, we may rewrite
this latter limit a8
, ix.) Seven indeterminate forms are dlscussed in this book They are
, o
symbohzedbyO/O oo/oo 0- ooa.nd’oo“‘"o O ‘ { ‘_OO
%(OJ—
O 5_ - x.) Tohandle / cos® z di, we first rewrite it as _
- F
o0
@ r xi.) / - cosx dz does not converge because QLM%WB"" S&N- Q=
does not exist. b o4
/o fcm X
(' xn)/ a—--dmconvergesfiandonlylf ' m bflOO *
| 1 _
xiii.) The integral —— dx does not exist in the proper sense
DS¢ because the function o1
f(z) = assumes arbitrarily large
values near the point Lf
2. (a) Find the exact value of log; 27. = 4
9
(b) Solve for z:
2 i | 63—593 =4,
