Question

lim x->infinity [ (a^x)/{(a^x)+1} ]

Answer 1

calculus 2?

Answer 2

1

Answer 3

it is also given a>0.

Answer 4

Multiply top and bottom by \[\frac{1}{a^x}\]

Answer 5

This is a rational functions problem you might have seen in precalc.

Since the degree of the numerator will always be the same as the degree of the denominator as x --> infinity, the function goes to the ratio of the coefficients of the highest degree term of the top and bottom of the fraction.

Answer 6

1

Answer 7

which is 1

Answer 8

\[\frac{1}{1+ \frac{1}{a^x}}\]

Answer 9

the second term in bottom goes to zero

Answer 10

we can't say anything about a^x ...because we don't know about "a".(other than only a>0)

Answer 11

if suppose a=1 then what will happen......i think we will get 1/2