Question

The value of `lim_(xrarr oo)(sqrt(3x^2-1)+sqrt(2x^2-1))/(4x+3)`, is
A. `(sqrt(3)-sqrt(2))/(4)`
B. `(1)/(4(sqrt(3)-sqrt(2)))`
C. `(sqrt(3)-sqrt(2))/(2)`
D. none of these

Answer 1

Correct Answer - B
Dividing each term in the numerator and denominator by x, we get
`lim_(x to oo) (sqrt(3x^2-1)|sqrt(2x^2-1))/(4x+3)`
`=lim_(x to oo)(sqrt(3-x//^2)+sqrt(2-1//x^2))/(4+3//x)=(sqrt(2-x//x^2))/(4)=(1)/(4(sqrt(3)-sqrt(2)))`