limit of (10^8)(x^5) + (10^6)(x^4)+ (10^4)(x^2) / ....

[tsh44]

Hi I am having trouble with this particular limit

lim
xapproaches infinity

(10^8)(x^5) + (10^6)(x^4)+ (10^4)(x^2) / (10^9)(x^6) + (10^7)(x^5) + (10^5)(X^3)

 

[pka]

Note that the degree of the denominator exceeds that of the numerator.
Divide both by \(\displaystyle x^6\).

 

[stapel]

(10^8)(x^5) + (10^6)(x^4)+ (10^4)(x^2) / (10^9)(x^6) + (10^7)(x^5) + (10^5)(X^3)

I will guess that you mean "x" and "X" to actually be the same variable (contrary to standard mathematical practice), But please note that tthe above means the following:

. . . . .10⁸x⁵ + 10⁶x⁴ + (10⁴x²) / (10⁹x⁶) + 10⁷x⁵ + 10⁵x³

In other words:

. . . . .\(\displaystyle \L 10^8 x^5\, +\, 10^6 x^4\, +\, \frac{10^4 x^2}{10^9 x^6}\, +\, 10^7 x^5\, +\, 10^5 x^3\)

Is this what you meant? Or did you mean something more like the following?

. . . . .[10⁸x⁵ + 10⁶x⁴ + 10⁴x²] / [10⁹x⁶ + 10⁷x⁵ + 10⁵x³]

In other words:

. . . . .\(\displaystyle \L \frac{10^8 x^5\, +\, 10^6 x^4\, +\, 10^4 x^2}{10^9 x^6\, +\, 10^7 x^5\, +\, 10^5 x^3}\)

Please confirm or correct. When you reply, please include all of your work and reasoning so far. Thank you.

Eliz.

 

[tsh44]

Sorry for not making that clear. I meant
[(10^8)(x^5) + (10^6)(x^4) + (10^4)(x^2)] / [(10^9)(x^6) + (10^7)(x^5) + (10^5)(x^3)]

pka said to divide by (x^6). So would that just leave 1/ 10^9 left?

 

[stapel]

pka said to divide by (x^6). So would that just leave 1/ 10^9 left?

How are you getting that?

Please be specific. Thank you.

Eliz.

 

[tsh44]

I believe you get 0 because the denominator is larger than the numerator

 

[skeeter]

I believe you get 0 because the denominator is larger in degree than the numerator

bingo!