Question

lim x→∞ x[sqrt(x^2-2x + 5)- abs(x-1)], will this approach to infinity or 2, can you explain. Thank you!

Answer 1

infinity i'd say..

Answer 2

ohhh i havent seen x in front of the [ ]

Answer 3

had x been tending -inf ..i guess ans would have been 2.

Answer 4

why you said that ? why dont you think its 2 ?

Answer 5

for the explanation part..

since x->+ infinity
|x-1| = x-1

now rationalize the numerator..

in the end, cancel out x from numerator and denom..

in the end, you'd be left with 4/0 form,,
where its not exactly 0 but it tends to 0 in the denominator..

thus it should be infinity..

Answer 6

but i left with 2 in the denominator

Answer 7

4x / [sqrt(x^2-2x+5) + (x-1)]

divide num and denom by x

4 / [sqrt(1 - 2/x + 5/x^2) + 1 - 1/x]
4 / 2

Answer 8

ohh..lol..yes..you're right..
4/2 it'll be..
really sorry..

Answer 9

i made an amateur sign mistake..sorry again..

Answer 10

so 2 it'll be..

Answer 11

Thank you! Thank you so much!! Finally understand it now!!!