Limits Involving Greatest Integer and Fractional Part

JEE Main Mathematics · Limits · 6 questions, latest first

• Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which lim_x →…202529 January, Shift 1 · Q24
• Let f(x)={ x-1, x is even, 2 x, x is odd, x ∈ N.. If for some a ∈ N, f(f(f(a)))=21, then lim_x → a^-{(|x|^3)/a-[x/a]}, where [t]…20241 February, Shift 2 · Q9
• Let {x} denote the fractional part of x and f(x)=(cos^-1(1-{x}^2) sin^-1(1-{x}))/({x}-{x}^3), x ≠ 0. If L and R respectively…20241 February, Shift 1 · Q26
• Let f, g and h be the real valued functions defined on R as f(x)={ x/(|x|), x ≠ 0; 1, x=0, g(x)= {(sin (x+1))/((x+1)), x ≠-1; 1,…202330 January, Shift 2 · Q68
• Let x=2 be a root of the equation x^2+p x+q=0 and f(x)= {(1- cos (x^2-4 p x+q^2+8 q+16))/((x-2 p)^4), x ≠ 2 p; 0, x=2 p} Then…202329 January, Shift 1 · Q67
• The set of all values of a for which lim_x → a([x-5]-[2 x+2])=0, where [∝] denotes the greatest integer less than or equal to ∝…202324 January, Shift 2 · Q70