Question

I'm having trouble evaluating this limit. My problem solving has become circular:

lim 1/t(sqrt(1+t)) - 1/t
t->0

Answer 1

[1 - sqrt(1+t)]/t

Answer 2

now multiply and divide by (1+sqrt(1+t))

Answer 3

\[\frac1t (\frac{1-\sqrt{1+t}}{\sqrt{1+t}})=\frac 1t{\frac{-t}{\sqrt{1+t}*(1+\sqrt{1+t})}}\]
-1/sqrt(1+sqrt(2)

Answer 4

Is this right? I tried this on a limit calculator and it came up -1/2 and I couldn't understand how that answer was arrived at

Answer 5

no its indeed -1/2

Answer 6

just take the expression \[\frac1t {\frac{-t}{\sqrt{1+t}*(1+\sqrt{1+t})}}\]put t=0 here u get\[\frac{-1}{\sqrt1*(1+\sqrt1)}=-\frac 12\]sorry for the mistake i did . i just did some wrong manipulation..

Answer 7

Do you happen to have the entire solution so that I can follow it step by step. I know it's asking for a lot. I'm just a bit confused.

Answer 8

which u have problem..i can explain.

Answer 9

What is the least common denominator? in the first algebraic step?

Answer 10

did u understand my very first post.?

Answer 11

Okay so the question is

lim t->0 1/t*sqrt(1+t) - 1/t

Answer 12

What I did was multiply each term by

Answer 13

by t(tsqrt(t+t))/t(tsqrt(t+t))

Answer 14

\[\frac1{t \sqrt{1+t}}-\frac1t=\frac1t(\frac1{\sqrt{1+t}}-1)\]\[=\frac1t* \frac{1-\sqrt{1+t}}{\sqrt{1+t}}\] multiply both numerator and deno with 1+sqrt(1+t) u will get\[\frac1t \frac{1-(1+t)}{\sqrt{1+t}*(1+\sqrt{1+t})}\]\[\frac1t \frac{-t}{\sqrt{1+t}*(1+\sqrt{1+t})}\]\[=\frac{-1}{\sqrt{1+t}*(1+\sqrt{1+t})}\]

Answer 15

now did u get it??

Answer 16

Holy cow. Now I really feel stupid. Thank you so much

Answer 17

you most welcome........