Limits Using Newton-Leibnitz Formula

JEE Main Mathematics · Limits · 6 questions, latest first

• lim_x → (π)/2((∫_x^3^(π / 2)^3( sin (2 t^1 / 3)+ cos (t^1 / 3)) d t)/((x-(π)/2)^2)) is equal to20249 April, Shift 2 · Q9
• Let f(x)=∫_0^x(t+ sin (1-e^t)) d t, x ∈ R. Then, lim_x → 0 (f(x))/x^3 is equal to20244 April, Shift 2 · Q9
• 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…202430 January, Shift 1 · Q8
• Let the slope of the line 45 x+5 y+3=0 be 27 r_1+(9 r_2)/2 for some r_1, r_2 ∈ R. Then lim_x → 3(∫_3^x (8 t^2)/((3 r_2 x)/2-r_2…202429 January, Shift 2 · Q25
• lim_x → (π)/2(1/((x-(π)/2)^2) ∫_x^3^((π)/2)^3 cos (t^(1/3)) d t) is equal to202429 January, Shift 1 · Q8
• lim_x → 0 48/x^4 ∫_0^x (t^3)/(t^6+1) d t is equal to ____.202330 January, Shift 1 · Q86