Evaluate the following limits. If needed, enter '101' for ∞ and '-101' for −∞.
$$\lim_{x \rightarrow \infty} \left( \sqrt{x^2 + 9 x + 1} -x \right) $$
i want to see the algebraic solution thx

Question

Evaluate the following limits. If needed, enter '101' for ∞ and '-101' for −∞.
$$\lim_{x \rightarrow \infty} \left( \sqrt{x^2 + 9 x + 1} -x \right) $$
i want to see the algebraic solution thx

anonymous · Answer

rationalize it

anonymous · Answer

yea, its like (x^2+9x+1)^(1/2) -x and then???

anonymous · Answer

do you know how to rationalize a eqn??
PS- divide and multiply by  (x^2+9x+1)^(1/2) +x 
x^2 will vanish out from num after multiplication then take x common from the denom and cancel out x term

anonymous · Answer

oh yea its +x
and then.... what do u mean "x^2 will vanish out from num after multiplication then take x common from the denom and cancel out x term"?

anonymous · Answer

in the num its kind of multiplication of (a+b)(a-b)= a^2- b^2.....putting those  equations you'll realize x^2 will vanish out

anonymous · Answer

any idea what am trying to say?

anonymous · Answer

oh yea ic!!!

anonymous · Answer

so ques solved?

anonymous · Answer

yes
thank u !!