Limit questions
411 published questions with worked solutions.
- Let and be the distinct roots of ax^2 + bx + c = 0, then _ x 1 - (ax^2 + bx + c ) (x - )^2 is equal to
- Let f : R R be a positive increasing function with _ x f(3x) f(x) = 1. Then _ x f(2x) f(x) =
- _ x 2 ( 1 - 2(x - 2) x - 2 )
- The value of _ x 0 x |x|+x^2 is
- Let (a) and (a) be the roots of the equation ( [3] 1+a -1 )x^2+ ( 1+a -1 )x+ ( [6] 1+a -1 )=0 where a>-1 then _ a 0^+ (a) and _ a...
- If _ x 1 x^2 - ax + b x - 1 = 7, then a + b is equal to
- _ x 0 (1- 2x)(3+ x) x 4x has the value
- _ x 0 2x |x|+x^2 =
- _ x 0 ( 1+ x 1+ x )^ cosec ,x =
- _ x 0 27^x - 9^x - 3^x + 1 5 - 4 + x =
- _ x [ 8x^2+5x+3 2x^2-7x-5 ]^ 4x+3 8x-1 =
- _ x 2 ( 5x-8 8-3x )^ 3 2x-4 =
- _ x 0 (1 - 2x) 5x x^2 3x is
- _ x 2 (1- x)(8x^3- ^3) x ( -2x)^4
- _ x a a + 2x - 3x 3a + x - 2 x = _____.
- The value of _ x a a+2x - 3x 3a+x -2 x is
- If S_1= _ r=1 ^ n r, S_2= _ r=1 ^ n r^2, and S_3= _ r=1 ^ n r^3, then the value of _ n S_1 (1+ S_3 4 ) S_2^2 is
- _ n n ( n^2+9 -n )=
- The quadratic equation whose roots are m and n, where m = _ x 0 x (1 + 2x) x x and n = _ x 0 x + ( 1 + x x ) x , is
- _ x 1 [ x-2 x^2-x - 1 x^3-3x^2+2x ]=
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