Calculate lim t- negative infinity ((2t^2 - t -2)^1/2) / (2t+1)

Question

Calculate lim t-> negative infinity  ((2t^2 - t -2)^1/2) / (2t+1)

amistre64 · Answer

x = sqrt(x^2) ... might be useful

zned6559 · Answer

I know the answer is -1/sqrt 2 but I don't know how to get there

amistre64 · Answer

^(1/2) is the same as sqrt()

id put them both under the sqrt and compare them

amistre64 · Answer

$$\frac{\sqrt{2t^2-t-1}}{\sqrt{(2t+1)^2}}$$

zned6559 · Answer

the bottom is suppose to be 2t+1
no sqrt

amistre64 · Answer

what does sqrt(x^2) reduce to?

zned6559 · Answer

x

amistre64 · Answer

then sqrt((2t+1)^2) = 2t+1

zned6559 · Answer

$$\sqrt{2t ^{2}-t-2}\div2t+1$$

amistre64 · Answer

you are not seeing the obvious ... 

$$\sqrt{2t ^{2}-t-2}\div2t+1$$
$$\sqrt{2t ^{2}-t-2}\div \sqrt{(2t+1)^2}$$

amistre64 · Answer

what is the expansion of (2t+1)^2 ?

zned6559 · Answer

$$4t ^{2}+4t+1$$

amistre64 · Answer

then we have
$$\sqrt{\frac{2t^2-t-2}{4t^2+4t+1}}$$

amistre64 · Answer

what do we know about polynomials and their limits?

zned6559 · Answer

not sure

amistre64 · Answer

then you need to cover some of your basic rules .... not sure what theyve covered tho

amistre64 · Answer

polys of the same degree, limit to their leading coeffs

zned6559 · Answer

I got it now!

amistre64 · Answer

the only thing to watch for is the sign, by squaring the bottom we altered the sign of it inthe process.

amistre64 · Answer

2t+1 as t to -inf is a negative value .... so we are originally going to have a negative limit in the end