_------...(Jf--,.-
-_-..
...
;-:::..;._
Calculus
1,
Test
2, (130)
Calculus
1,
Sections
3.1-4.3
--~,_/-----
.......
__
._.,,~.,.----.-
Instructions
to
students:
The
test
is out of (120). There are
lQ
points
for
extra
credit. Please show all your calculations.
No
calculators' may be
used. Show all your calculations. Partial credit will be given for all correct
calculations. Good lucid
Question
1-(30)
(a) Using first principles, calculate
the
derivative of the following function.
Show all your calculations.
f(x)
=
JX=l
(b) Explain carefully why
f(x)
=
Ixl
is continuous
at
O.
(c) Explain carefully why
f(x)
=
Ixl
is
not
differentiable at
O.
Question
2-(30)
Using rules
for
derivatives, calculate
the
derivatives of
the
following func-
tions. Show all your calculations.
(a) 2
x
f(x)
= 3;);2 -
2:1:
+ 1
(b)
f(x)
= V
sin3
(x) + 1 + 100 +
X;/4
(
c)
Find an equation of the tangent line
to
the
curve
at
the
point (1,1/2).
Question
3-(30)
(a) Find
yl
if sin(x + y) = y2cos(x).
1
