Sunday

February 1, 2015

February 1, 2015

Posted by **John** on Saturday, November 22, 2008 at 11:54pm.

- Calculus -
**drwls**, Sunday, November 23, 2008 at 12:16amIt depends upon whether you take the positive or negative square root. If you take the positive root and x-> -infinity, the first term approaches = |x| = -x (for negative x). Adding x to that gives you zero in the limit.

Check, let x = -1000

sqrt(10^6 -3000)= 999.5

Subtract -1000 and you get -0.5

Let x = -10,000

sqrt(10^8- 3^10^4) = 999.85

Suntract -10,000 and you get -0.15

- Calculus -
**John**, Sunday, November 23, 2008 at 12:40amI still don't get it. The answer is -1.5, how do I get that w/o a calculator?

- Calculus -
- Calculus -
**drwls**, Sunday, November 23, 2008 at 6:29amYou are correct, both my derivation and my numerical examples were wrong. You can get -1.5 by considering a series expansion of sqrt(1+y) = 1 + y/2 + ...

sqrt(x^2 + 3x) = sqrt[x^2*(1 + (3/x)]

= x * [1 + (3/2)x + higher order terms in 3/x] = x + 3/2 + ...

As x approaches -infinity, with positive square roots only taken, the first term sqrt(x^2) approaches |x| and the second term remains -3/2

Adding x to that is like subtracting

-|x|, leaving you with -3/2

Fox x = -1000, f(x) = -1.5011

for x = -10000, f(x) = -1.5001

I apologize for my sloppy math.

**Answer this Question**

**Related Questions**

Calculus - What is the limit? 1. limit as x goes to POSITIVE infinity (10x+8)/(...

AP Calculus - For which of these functions f(x) does limit as x approaches ...

Calculus - For which of these functions f(x) does limit as x approaches negative...

calculus - What is the limit of the function as x approaches infinity? 4x^4 - 4^...

calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...

Calculus - i was just wondering if the limit of a funtion exists as it ...

Calculus - 1.Evaluate: (1/(x*sqrt(x^2-4)) I know the answer is -1/2*arctan(2/...

Calculus - what is the limit as x goes to infinity of (8x^3-10x^2-2x)/(3-10x-11x...

Calculus - what is the limit as x goes to infinity of (8x^3-10x^2-2x)/(3-10x-11x...

Calculus - Find limit as x approaches 1 5/(x-1)^2 A. 0 B. Negative infinity C. 5...