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e^(x) and ln asymptotes

How do i find the asymptotes for these fuctions?

For example: 144-36e^(-2x)

How do i find the horizontal asymptote for this?

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Reply 1

brianeverit

Original post by QuantumSuicide

How do i find the asymptotes for these fuctions?

For example: 144-36e^(-2x)

How do i find the horizontal asymptote for this?

Posted from TSR Mobile

Investigate to see what happens to trhe value of the function as x tends to infinity.
In the example you have quoted,

e^{-2x}

will get smaller and smaller as x gets larger and so will tend to zero. hence the asymptote in this case would be y=144.

Reply 2

alexmufc1995

Original post by QuantumSuicide

How do i find the asymptotes for these fuctions?

For example: 144-36e^(-2x)

How do i find the horizontal asymptote for this?

Posted from TSR Mobile

Test increasingly large negative and positive values of x

As x becomes negative and large, e^(-2x) becomes increasingly large, so f(x) becomes increasingly negative - no asymptote.

As x becomes positive and large, e^(-2x) becomes increasingly small, so f(x) approaches 144 - hence y=144 is an asymptote

EDIT: See above, beaten to it!

(edited 10 years ago)

Reply 3

QuantumSuicide

Original post by brianeverit

Investigate to see what happens to trhe value of the function as x tends to infinity.
In the example you have quoted,

e^{-2x}

will get smaller and smaller as x gets larger and so will tend to zero. hence the asymptote in this case would be y=144.

I see. Is the method the same for finding vertical asymptotes and the function lnx?

Posted from TSR Mobile

Reply 4

IgorYakov

Original post by QuantumSuicide

How do i find the asymptotes for these fuctions?

For example: 144-36e^(-2x)

How do i find the horizontal asymptote for this?

Posted from TSR Mobile