Limit questions
411 published questions with worked solutions.
- _ x 2 [2-x]+[x-2]-x
- _ x -1 [x]+|x| , where [ ] denotes the greatest integer function,
- If f(x)= cases [x] [x] , & [x] 0 [2mm] 0, & [x]=0 cases , where [ ] denotes the greatest integer function, then _ x 0 f(x) is...
- _ x 0 _0^ x^2 t^2 ,dt x x is equal to
- _ x 1+0 _1^x|t-1| ,dt (x-1) is equal to
- If f(x) is continuous in [0,1] and f ( 13 )=1 then _ n f ( n 9n^2+1 ) is
- If f(x) is continuous and f ( 92 )= 29 then _ x 0 f ( 1- 3x x^2 ) is equal to
- Let f(x)= cases 1+ 2x a , & 0 x<1 [2mm] ax, & 1 x<2. cases If _ x 1 f(x) exists then a is
- If is a repeated root of ax^2+bx+c=0 then _ x (ax^2+bx+c) (x- )^2 is
- If _ n (an- 1+n^2 1+n )=b, a finite number, then
- _ n n! (kn)^n ^ 1/n , where k 0 is a constant and n N, is equal to
- _ x 12 3[x] [x] , where [x] denotes the greatest integer x, is equal to
- If f(x) = _ =1 ^ n (x - 1 ) (x - 1 +1 ) then _ n f(0) is
- If f(x + 2) = 12 f(x + 1) + 4 f(x) and f(x) > 0 for all x R then _ x f(x) is
- If _ x 0 (a-n)nx- x nx x^2 =0, n 0 then a is equal to
- Given f'(x)=6 and f'(1)=4, _ h 0 f(2h+2+h^2)-f(2) f(h-h^2+1)-f(1) is
- Let and be the distinct roots of ax^2+bx+c=0 then _ n 1- (ax^2+bx+c) (x- )^2 is equal to
- _ x - x^3-x 1+x^6 is equal to
- If _ x a x _a^x f(x) ,dx x - a = a^3 + a^2 (a 0) then f(2a) is
- For x R, _ x ( x - 3 x + 2 )^ x is equal to
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