How do you find the limit $\frac{1 - \frac{t}{t - 1}}{1 - \sqrt{\frac{t}{t - 1}}}$ $(1-t/(t-1))/(1-sqrt(t/(t-1))$ as $x \to \infty$ $x->oo$ ?

Question

1251 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-19T10:40:37

2

Use $(a - b) (a + b) = a^{2} - b^{2}$ $(a-b)(a+b)=a^2-b^2$ .

The given function is

$(1 + \sqrt{\frac{t}{t - 1}}) \frac{1 - \sqrt{\frac{t}{t - 1}}}{1 - \sqrt{\frac{t}{t - 1}}}$ $(1+sqrt(t/(t-1)))(1-sqrt(t/(t-1)))/(1-sqrt(t/(t-1)))$

$= 1 + \sqrt{\frac{t}{t - 1}}$ $=1+sqrt(t/(t-1))$

$= 1 + \sqrt{\frac{1}{1 - \frac{1}{t}}} \to 1 + 1 = 2$ $=1+sqrt(1/(1-1/t)) to 1+1=2$ , as $t \to \infty$ $t to oo$

How do you find the limit (1-t/(t-1))/(1-sqrt(t/(t-1))1−tt−11−√tt−1(1-t/(t-1))/(1-sqrt(t/(t-1)) as x->oox→∞x->oo?