Use algebraic manipulations to evaluate lim as x approaches infinity:
f(x)=((x^2)+2x-1)/(3+3(x^2))

Question

Use  algebraic manipulations to evaluate lim as x approaches infinity:  
f(x)=((x^2)+2x-1)/(3+3(x^2))

anonymous · Answer

$$(\frac{x ^{2} + 2x - 1 }{ 3 + 3x ^{2} }) (\frac{ \frac{ 1 }{ x ^{2} } }{ \frac{ 1 }{ x ^{2} } })$$
$$\frac{ 1 + \frac{ 2 }{ x }  - \frac{ 1 }{ x ^{2} }}{ \frac{ 3 }{ x ^{2} } + 3 }$$

then determine lim as x approaches infinity

since N/(infinity) is 0

$$\frac{ 1+ 0 -0 }{ 0+3 }$$

so the answer is $$\frac{ 1 }{ 3 }$$

try checking my answer too, i might have missed something

anonymous · Answer

Thank you! The answer is 1/3 I just didn't know how to evaluate infinity.

anonymous · Answer

just always divide first the equation by the variable having the highest exponent

anonymous · Answer

Do you mean in general or when I am talking about infinity?  I used the properties of limits to find the limit in each part and then was going to do the math but wasn't sure what value infinity represented.

anonymous · Answer

only when you're talkin' 'bout infitity