Question

lim(x->infinity)   {(√x²+a²) - (√x²+b²)}÷{(√x²+c²) - (√x²+d²)}
A) (a²-b²)÷(c²-d²)                B) (a²+b²)÷(c²-d²)                    C) (a²+b²)÷(c²+d²)                          
D) None of these 

Answer 1

rationalise numerator & denominator we get
lim         (a²-b²){(√x²+c²) + (√x²+d²)} ÷ (c²-d²){(√x²+a²) + (√x²+b²)}
x------>∞
(a²-b²)/(c²-d²) lim           {(√1+c²/x²) + (√1+d²/x²)} ÷ {(√1+a²/x²) + (√1+b²/x²)}
                  x------->∞
= (a²-b²)/(c²-d²) {(1+1)/(1+1)}                    (a²/x² = a²/∞² = 0 & so on for b,c,d)
= (a²-b²)/(c²-d²)
hence (A) option is correct

Answer 2

Answer:

A) (a^2 - b^2)÷(c^2 - d^2)