Evaluate the following limit : lim(x→∞) (√(x^2 + a^2) + √(x^2 + b^2))/(√(x^2 + c^2) + √(x^2 + d^2))

Question

Evaluate the following limit : \(\lim\limits_{\text x \to \infty}\cfrac{\sqrt{\text x^2+a^2}+\sqrt{\text x^2+b^2}}{\sqrt{\text x^2+c^2}+\sqrt{\text x^2+d^2}} \)

lim(x→∞) (√(x² + a²) + √(x² + b²))/(√(x² + c²) + √(x² + d²))

Answer 1

Given: \(\lim\limits_{\text x \to \infty}\cfrac{\sqrt{\text x^2+a^2}+\sqrt{\text x^2+b^2}}{\sqrt{\text x^2+c^2}+\sqrt{\text x^2+d^2}} \)

Rationalizing the numerator and denominator we get,

Hence,