Limit questions
411 published questions with worked solutions.
- Let f(x)= cases 1+ x 2k , & 0<x<2 kx, & 2 x<4 cases If _ x 2 f(x) exists, then what is the value of k?
- If f(x)= [x] |x| , x 0, where [ ] denotes the greatest integer function, then what is the right-hand limit of f(x) at x=1?
- Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit _ x 0^+ (1-x)^ 1 x...
- The value of the limit _ x 2 4 2 ( 3x + x) (2 2x 3x 2 + 5x 2 ) - ( 2 + 2 2x + 3x 2 ) is _____
- Let be a positive real number. Let f: R R and g: ( , ) R be the functions defined by f(x) = ( x 12 ) and g(x) = 2 _e ( x - ) _e...
- If = _ x 0 e^ x^3 - (1 - x^3)^ 1 3 + ((1 - x^2)^ 1 2 - 1 ) x x ^2 x , then the value of 6 is _____.
- Let f: (0, 1) R be the function defined as f(x) = n if x [ 1 n+1 , 1 n ) where n N . Let g: (0, 1) R be a function such that _...
- Let f(x) be a continuously differentiable function on the interval (0, ) such that f(1) = 2 and _ t x t^ 10 f(x) - x^ 10 f(t) t^9...
- Let k R . If _ x 0+ ( ( kx) + x + x )^ 2 x = e^6, then the value of k is
- Let S be the set of all ( , ) R R such that _ x (x^2)( _e x)^ ( 1 x^2 ) x^ ( _e(1 + x))^ = 0. Then which of the following is...
- Let a be an integer such that _ x 7 (18 − [1 − x])/([x − 3a]) exists, where [t] is greatest integer t. Then a is equal to :
- _ x 0 ((x + 2 x)^ 3 + 2(x + 2 x)^ 2 + 3 (x + 2cosx))/((x + 2)^ 3 + 2(x + 2)^ 2 + 3 (x + 2)))^ 100/x is equal to _____ .
- If _ x 1 ( (3x^ 2 - 4x + 1) - x^ 2 + 1)/(2x^ 3 - 7x^ 2 + ax + b) = −2, then the value of (a − b) is equal to _____ .
- If _ x 0 ( e^ x + e^ -x + sin x)/(x ^ 2 x) = 2/3, where , , R, then which of the following is NOT correct ?
- The value of _ x 1 ((x^ 2 - 1) ^ 2 ( x))/(x^ 4 - 2x^ 3 + 2x - 1) is equal to
- _ x 0 1- ^34x x^2 is equal to
- If > >0 are the roots of the equation ax^2+bx+1=0, and _ x 1 ( 1- (x^2+bx+a) 2(1- x)^2 )^ 1/2 = 1 k ( 1 - 1 ), then k is equal to
- _ x 0 ( ( 1- ^2(3x) ^3(4x) ) ( ^3(4x) _e(2x+1)^5 ) ) is equal to ................
- If _ x 0 e^ ax - (bx)- cxe^ -cx 2 1- (2x) =17, then 5a^2+b^2 is equal to :
- The set of all values of for which _ x ([x-5]-[2x+2])=0, where [ ] denotes the greatest integer less than or equal to is equal to
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