lim as t approaches 0 of [(1/t(1+t)^1/2) -(1/t)]

Question

tkhunny · Answer

Have you considered adding the fractions?

$\dfrac{1 - \sqrt{1+t}}{t\cdot\sqrt{1+t}}$

Couple things that could be done, after that.

1) "Rationalize" the Numerator.
2) l'Hospital's Rule for form 0/0.

anonymous · Answer

Can you please show me how you got to that fraction right there. Just to clarify the original form is $$\frac{ 1 }{ t \sqrt{t+1} }-\frac{ 1 }{ t}$$ If that is what you used i'm confused how you got there.

dumbcow · Answer

he/she combined fractions

$$\frac{1}{t \sqrt{1+t}}-\frac{1 \sqrt{1+t}}{t \sqrt{1+t}} = \frac{1-\sqrt{1+t}}{t \sqrt{1+t}}$$

anonymous · Answer

oh ok you found a common denominator my bad i'm dumb

tkhunny · Answer

Common Denominator?  You've been doing it for a long time.  Don't forget things that you should know.

Truthfully, it's common for things you know to abandon you when you encounter something new.  You have to fight it!

anonymous · Answer

ok and then next would i multiply by conjugate?

dumbcow · Answer

yes that would be my suggestion

anonymous · Answer

ok thanks guys

dumbcow · Answer

you should end up with limit of -1/2

anonymous · Answer

awesome thanks