Mathematics · 2023
JEE Main · 30 January 2023, Shift 1 · Q86
lim_x → 0 48/x^4 ∫_0^x (t^3)/(t^6+1) d t is equal to ____.
$\displaystyle \lim _{x \rightarrow 0} \frac{48}{x^4} \int_0^x \frac{\mathrm{t}^3}{\mathrm{t}^6+1} \mathrm{~d} t$ is equal to $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
12
More from Limits
- 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^32023
- The value of lim_x → 0 (log_e( sec (e x) · sec (e^2 x) · … · sec (e^10 x)))/(e^2-e^2 cos x) is equal to2026
- 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:2025
- Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which lim_x →…2025
- If lim_x → 0 (e^(a-1) x+2 cos b x+(c-2) e^-x)/(x cos x- log_e(1+x))=2, then a^2+b^2+c^2 is equal to:2026
- Let f:[-(π)/2, (π)/2] → R be a differentiable function such that f(0)=1/2. If the lim_x → 0 (x ∫_0^x f(t) d t)/(e^x^2-1)=α, then 8 α^2 is equal to:2024
- lim_t → 0(1^(1/(sin^2 t))+2^(1/(sin^2 t))+…+n^(1/(sin^2 t)))^sin^2 t is equal to2023
- For α, β, γ ∈ R, if lim_x → 0 (x^2 sin α x+(γ-1) e^x^2)/(sin 2 x-β x)=3, then β+γ-α is equal to:2025
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.