Graph #1: Function calculator

You have entered: f (x) = sin(x).

y = f(x) = sin(x) ,

for all x in [ – 6.28 , + 6.28 ] = [ 2pi, 2pi ]

Graph #2: Function calculator

You have entered: f (x) = cos(x).

y = f(x) = cos(x) ,

for all x in [ – 6.28 , + 6.28 ] = [ -2pi, 2pi ]

Graph #3: Function calculator

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 .

Graph #4: Function calculator

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 .

Graph #5: Function calculator

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 .

Graph #6: Function calculator

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 .

Graph #7: Function calculator

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.

Graph #8: Function calculator

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 .

Graph #9: Function calculator

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

Graph #10: Function calculator

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

Graph #11: Function calculator

You have entered: f (x) = sin(1/x).

y = f(x) = sin(1/x) ,

for all x in [ – 1 , + 1 ]

Graph #12: Function calculator

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.

Graph #13: Function calculator

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.

Graph #14: Function calculator

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.