J joy08 New member Joined Dec 31, 2007 Messages 12 Dec 31, 2007 #1 I'm having trouble with finding the limit for this problem. Find the limit : lim x-> -(negative) infinity (x+?x^2+3x)
I'm having trouble with finding the limit for this problem. Find the limit : lim x-> -(negative) infinity (x+?x^2+3x)
D Deleted member 4993 Guest Dec 31, 2007 #2 Re: Ap calculus joy08 said: I'm having trouble with finding the limit for this problem. Find the limit : lim x-> -(negative) infinity (x+?x^2+3x) Click to expand... This is a tricky one.... Hint: The answer is -3/2 First multiply and divide by (x-?x^2+3x) Then let x = -m and let m -> +infinity
Re: Ap calculus joy08 said: I'm having trouble with finding the limit for this problem. Find the limit : lim x-> -(negative) infinity (x+?x^2+3x) Click to expand... This is a tricky one.... Hint: The answer is -3/2 First multiply and divide by (x-?x^2+3x) Then let x = -m and let m -> +infinity
O o_O Full Member Joined Oct 20, 2007 Messages 393 Jan 1, 2008 #3 Re: Ap calculus Mmm I don't think substitution is necessary. \(\displaystyle \lim_{x \to -\infty} \left( \left(x + \sqrt{x^{2} + 3x}\right) \cdot \frac{x - \sqrt{x^{2} + 3x}}{x - \sqrt{x^{2} + 3x}} \right)\) \(\displaystyle \lim_{x \to -\infty} \left(\frac{x^{2} - x^{2} - 3x}{x - \sqrt{x^{2} + 3x}} \right)\) \(\displaystyle \lim_{x \to -\infty} \left( \frac{-3x}{x - \sqrt{x^{2} + 3x}} \right)\) Then multiply top and bottom by \(\displaystyle \frac{1}{x}\) keeping in mind that x is negative so: \(\displaystyle x = - |x| = -\sqrt{x^{2}}\)
Re: Ap calculus Mmm I don't think substitution is necessary. \(\displaystyle \lim_{x \to -\infty} \left( \left(x + \sqrt{x^{2} + 3x}\right) \cdot \frac{x - \sqrt{x^{2} + 3x}}{x - \sqrt{x^{2} + 3x}} \right)\) \(\displaystyle \lim_{x \to -\infty} \left(\frac{x^{2} - x^{2} - 3x}{x - \sqrt{x^{2} + 3x}} \right)\) \(\displaystyle \lim_{x \to -\infty} \left( \frac{-3x}{x - \sqrt{x^{2} + 3x}} \right)\) Then multiply top and bottom by \(\displaystyle \frac{1}{x}\) keeping in mind that x is negative so: \(\displaystyle x = - |x| = -\sqrt{x^{2}}\)
