be the Function (in the picture) a,b are Positive, is known that y=1 is a Horizontal Asymptote OF the Function :limf(x)=9 when x-->o+.

I got this answers and I need to know what is the sum of a+b:

1)3
2)4
3)5
4)6
5)7
thanks.

I think you have an error here. Given the fiunction:



The limit as x approaches infinity is:



So if the limit approaches y = 1, then you know that It does not matter what the value of b is.

**EDIT** Unfortunately I solved the wrong problem! Sorry 'bout that.

Since we are told there is a horizontal asymptote, then we must have:



If we evaluate this limit it is



But we were told this limit is 1, so





Expanding f(x) gives us a term which is:

(all other terms tend to 0 as x approaches 0).

Since x=0 and this term must equal 9, then:



The value of b determines how high up the y-axis the graph goes.

For instance, if b=4, then

Thus, the sum is 4.

Ahh , I misread the post! I thought it was (a) the limit going to infinity (not 0) and (b) I read "xln(x) as "sin(x)." It's neen a long day...

Quote:

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I read "xln(x) as "sin(x)."

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You know, I done that as well. :confused:

Then, I looked again and saw the xlnx.

Thanks to both of you and yes we all mistake sometime :-)

Still thank you People.