Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).

Question

Quizplus · Accepted Answer

By multiplying and dividing the expression by the conjugate expression (sqrt(4x^2+1)+2x), we get:
lim x->0 (sqrt(4x^2+1)-1)/(2x^2) * (sqrt(4x^2+1)+2x)/(sqrt(4x^2+1)+2x)
=lim x->0 ((4x^2)/(2x^2*(sqrt(4x^2+1)+2x)))= lim x->0 (2/(sqrt(4x^2+1)+2x))= 2/2=1
Therefore, the correct answer is D, 11eaa948_cdd7_e8e8_84bc_db7547ece3ea_TB2342_11.

Find the Limit Exactly (Hint: Multiply and Divide by the Conjugate