Limits at Infinity

JEE Main Mathematics · Limits · 2 questions, latest first

• Let f:(-∞, ∞)-{0} → R be a differentiable function such that f^′(1)= lim_a → ∞ a^2 f(1/a). Then lim_a → ∞ (a(a+1))/2…20246 April, Shift 1 · Q6
• lim_x → ∞ ((√(3 x+1)+√(3 x-1))^6+(√(3 x+1)-√(3 x-1))^6)/((x+√(x^2-1))^6+(x-√(x^2-1))^6) x^3202331 January, Shift 2 · Q66