Posted by **gibbs** on Friday, April 19, 2013 at 3:48am.

Evaluate the following limits:

(I) Lim. (x+1)/[1-sqrt(4+3x)]

X >-1

(II) Lim. (2-3x-5x^2)/(1+2x^2)

X >Infinite

- math -
**Reiny**, Friday, April 19, 2013 at 8:19am
rationalize the denominator

= (x+1)/[1-√(4+3x)] * (1 + √(4+3x))/(1 + √(4+3x))

= lim (x+1)(1 + √(4+3x))/ (1 - 4 - 3x)

= lim (x+1)(1 + √(4+3x))/ (-3(1+x)

= lim (1 + √(4+3x) )/-3 , as x -->-1

= -2/3

Lim. (2-3x-5x^2)/(1+2x^2) , X >Infinite

as x ---> infinity

the two terms that will "dominate" are -5x^2 on the top and 2x^2 at the bottom, the rest of the terms will become insignificant compared to their value

so we are left with -5x^2/(2x^2 or -5/2

so Lim. (2-3x-5x^2)/(1+2x^2)

X >Infinite

= -5/2

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