Continuity at a Point

JEE Main Mathematics · Continuity and Differentiability · 13 questions, latest first

• Let f(x)= lim_θ → 0((cos π x-x^(2/(θ)) sin (x-1))/(1+x^(2/(θ))(x-1))), x ∈ R. Consider the following two statements: (I) f(x) is…202628 January, Shift 2 · Q16
• Let [t] denote the greatest integer less than or equal to t. If the function f(x)= {b^2 sin ((π)/2[(π)/2( cos x+ sin x) cos x]),…202624 January, Shift 2 · Q16
• If f(x)= {(a|x|+x^2-2( sin |x|)( cos |x|))/x, x ≠ 0; b, x=0} is continuous at x=0, then a+b is equal to202623 January, Shift 2 · Q17
• Let f(x)= {(a x^2+2 a x+3)/(4 x^2+4 x-3), x ≠-3/2, 1/2; b, x=-3/2, 1/2} be continuous at x=-3/2. If f o f(x)=7/5, then x is equal…202623 January, Shift 1 · Q17
• Let f(x)= {(1+a x)^1 / x, x<0; 1+b, x=0; ((x+4)^1 / 2-2)/((x+c)^1 / 3-2), x>0} be continuous at x=0. Then e^a b c is equal to:20253 April, Shift 1 · Q17
• If the function f(x)= {2/x{ sin (k_1+1) x+ sin (k_2-1) x}, x<0; 4, x=0; 2/x log_e((2+k_1 x)/(2+k_2 x)), x>0} is continuous at…202523 January, Shift 1 · Q16
• Let f:(0, π) → R be a function given by f(x)= {(8/7)^((tan 8 x)/(tan 7 x)), 0<x<(π)/2; a-8, x=(π)/2; (1+| cot x|)^b/a| tan x|,…20249 April, Shift 1 · Q24
• For a, b>0, let f(x)= {(tan ((a+1) x)+b tan x)/x, x<0; 3, x=0; (√(a x+b^2 x^2)-√(a x))/(b √a x √x), x>0} be a continous function…20248 April, Shift 2 · Q9
• If the function f(x)= {(72^x-9^x-8^x+1)/(√2-√(1+ cos x)), x ≠ 0; a log_e 2 log_e 3, x=0} is continuous at x=0, then the value of…20244 April, Shift 2 · Q8
• Let f: R → R be a function given by f(x)= {(1- cos 2 x)/x^2, x<0; α, x=0, (β √(1- cos x))/x, x>0} where α, β ∈ R. If f is…20244 April, Shift 1 · Q6
• Let g(x) be a linear funchion and f(x)= {g(x), x ≤ 0; ((1+x)/(2+x))^(1/x), x>0}, is continuous at x=0. If f^′(1)=f(-1), then the…202431 January, Shift 1 · Q9
• Consider the function. f(x)= {(a(7 x-12-x^2))/(b|x^2-7 x+12|), x<3; 2^((sin (x-3))/(x-[x])), x>3; b, x=3,} where [x] denotes the…202427 January, Shift 1 · Q8
• If the function f(x)= {(1+| cos x|) (λ)/(| cos x|), 0<x<(π)/2; μ, x=(π)/2; (cot 6 x)/(e^cot 4 x), (π)/2<x<π} is continuous at…202325 January, Shift 2 · Q69