Find the borders lim x-->∞ (sqrt (4x^2+9x^4)+5x^2)/((2x-1)^2+2x) lim x-->-1 (sqrt(3+2x)-1)/(sqrt(5+x)-2) lim x-->∞ (sqrt (4x^2+9x^4)+5x^2)/((2x-1)^2+2x) lim x-->-1 (sqrt(3+2x)-1)/(sqrt(5+x)-2)

Expert Answers info

Luca B. eNotes educator | Certified Educator

calendarEducator since 2011

write5,348 answers

starTop subjects are Math, Science, and Business

You need to force factor `x^4`  under the square root such that:

`lim_(x-gtoo) (sqrt(x^4(4/x^2 + 9)) + 5x^2)/((2x-1)^2+2x)`

You need to force factor `x^2`  to numerator and denominator such that:

`lim_(x-gtoo) (x^2(sqrt(4/x^2 + 9) + 5))/(x^2((2-1/x)^2+2/x))`

You need to reduce by `x^2`  such that:

`lim_(x-gtoo) (sqrt(4/x^2 + 9) + 5)/((2-1/x)^2+2/x)`

Substituting `oo`  for x in limit equation yields:

`(sqrt(4/oo + 9) + 5)/((2-1/oo)^2+2/oo) = (sqrt(9) + 5)/(2+0)`

`lim_(x-gtoo) (sqrt(4/x^2 + 9) + 5)/((2-1/x)^2+2/x)= (3+5)/2`

`lim_(x-gtoo) (sqrt(4/x^2...

(The entire section contains 257 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

Ask a Question