Limits of the Form 1^∞

JEE Main Mathematics · Limits · 6 questions, latest first

• Let f be a differentiable function on R such that f(2)=1, f^′(2)=4. Let lim_x → 0(f(2+x))^3 / x=e^α. Then the number of times the…20254 April, Shift 2 · Q16
• If lim_x → 0((tan x)/x)^(1/x^2)=p, then 96 log_e p is equal to ____20253 April, Shift 2 · Q25
• If lim_t → 0(∫_0^1(3 x+5)^t d x)^(1/t)=(α)/(5 e)(8/5)^(2/3), then α is equal to ____.202529 January, Shift 2 · Q24
• lim_x → ∞ ((2 x^2-3 x+5)(3 x-1)^(x/2))/((3 x^2+5 x+4) √((3 x+2)^x)) is equal to:202523 January, Shift 2 · Q14
• If lim_x → ∞((e/(1-e))(1/e-x/(1+x)))^x=α, then the value of (log_e α)/(1+ log_e α) equals:202522 January, Shift 2 · Q16
• If α= lim_x → 0^+((e^√(tan x)-e^√x)/(√(tan x)-√x)) and β= lim_x → 0(1+ sin x)^1/2 cot x are the roots of the quadratic equation a…20248 April, Shift 2 · Q25