You have entered: f (x) = sin(x).
y = f(x) = sin(x) ,
for all x in [ 6.28 , + 6.28 ] = [
2pi, 2pi ]
You have entered: f (x) = cos(x).
y = f(x) = cos(x) ,
for all x in [ 6.28 , + 6.28 ] = [
-2pi, 2pi ]
You have entered: f (x) = 100-x2.
y =
f(x) = 100 x2 ,
y =
100 x2 < 0 for
all x < 10 ,
y =
100 x2 >= 0 for
all x in [ 10, 10] ,
y = 100 x2 < 0 for all x > + 10 .
You have entered: f (x) = abs(100-x2).
y =
f(x) = | 100 x2 | ,
y = f(x)
= | 100 x2 | =
( 100 x2 ) for all x
< 10
y = f(x)
= | 100 x2 | = +
( 100 x2 ) for all x
in [ 10, 10]
y = f(x)
= | 100 x2 | =
( 100 x2 ) for all x
> + 10 .
You have entered: f (x) = 1/x.
y = f(x) = 1 / x
,
for all x
in [ 5 , + 5 ]
The limit as x approaches 0+ of (1 / x) is infinity.
The limit as x approaches 0 of (1 / x) is ( infinity) .
The limit as x approaches ( infinity) of (1 / x) is L
= 0 .
The limit as x approaches infinity of (1 / x) is L = 0 .
You have entered: f (x) = sin(x).
y = f(x) = sin(x)
,
for
all x in [ 2 , + 2 ]
The limit as x approaches 0+ of (sin(x) / x) is
L = 1 .
The limit as x approaches 0 of (sin(x) / x) is L =
1 .
The limit as x approaches 0 + of (sin(x) / x) is L
= 1 .
You have entered: f (x) = sin(x)/x.
y = f(x) = sin(x)
/ x ,
for
all x in [ 2 , + 2 ]
The limit as x approaches 0 of (sin(x) / x) is L =
1.
You have entered: f (x) = ln(x).
y = f(x) = ln (x) ,
all x in [ 0 , 10 ]
The limit as x approaches 0+ of ln (x)
is infinity .
The limit as x approaches +infinity of ln (x)
is + infinity .
The limits as x approaches 0 or as x approaches ( infinity) of ln (x)
do not
exist because y = ln(x) is not defined when x
< 0 .
You have entered: f (x) = ln(x).
y = f(x) = ln (x) ,
all x in [
.5 , 3 ]
ln
1 =
0 and ln e
= ln
2.718281 . . . = 1
You have entered: f (x) = ln(abs(x)).
y = f(x) = ln (|x|)
all x in [ 3 ,
3 ]
ln |-1| = 0 ; ln |-e| = ln |-2.718281. . .| = 1
You have entered: f (x) = sin(1/x).
y = f(x) =
sin(1/x) ,
for
all x in [ 1 , + 1 ]
You have entered: f (x) = sin(1/x).
y = f(x) =
sin(1/x) ,
for
all x in [ .25, + .25]
The limit as x approaches 0 of ( sin(1/x) )
does not
exist, due to infinite oscillation.
You have entered: f (x) = x sin(1/x).
y = f(x) = x sin(1/x)
,
for
all x in [ .001,
+ .001]
The limit as x approaches 0 of (x sin(1/x) ) is L = 0.
You have entered: f (x) = x sin(1/x).
y = f(x) = x sin(1/x) ,
for
all x in [ 4 , + 4 ]
The limit as x approaches (+infinity) of (x
sin(1/x) ) is L =
1.
The limit as x approaches (-infinity) of (x
sin(1/x) ) is L =
1.
Note: To draw these graphs and others for yourself,
do the following:
Step #1: Click on the link shown in Step #4 and then
perform Steps #2 and #3.
Step #2: Click on the words online calculators and
plotters
Step #3: Click on the words function calculator
Step #4: To draw these
graphs and others for yourself, ==>
Click Here.