Limit questions
411 published questions with worked solutions.
- _ t 0 ( 1 1 ^2t + 1 2 ^2t + + 1 n ^2t )^ ^2t is equal to
- The value of _ n 1+2-3+4+5-6+ +(3n-2)+(3n-1)-3n 2n^4+4n+3 - n^4+5n+4 is :
- Let x = 2 be a root of the equation x^2+px+q=0 and f(x) - cases 1- (x^2-4px+q^2+8q+16) (x-2p)^4 , & x 2p 0, & x=2p cases Then _ x...
- Let f, g and h be the real valued functions defined of R as f(x) = cases x |x| , & x 0 1, & x=0 cases , g(x) = cases (x+1) (x+1)...
- _ x 0 48 x^4 _0^x t^3 t^6+1 dt is equal to___________.
- _ x ( 3x+1 + 3x-1 )^6+( 3x+1 - 3x-1 )^6 (x+ x^2-1 )^6+(x- x^2-1 )^6
- Let f and g be real valued functions defined on interval (−1, 1) such that g″(x) is continuous, g(0) ≠ 0, g′(0) = 0, g″(0) ≠ 0,...
- Let L = _ x 0 a - a^2 - x^2 - x^2 4 x^4 , a > 0. If L is finite, then
- Let α and β be the real numbers such that _ x 0 1 x^3 ( 2 _0^x 1 1 - t^2 ,dt + x x ) = 2. Then the value of α + β is _____.
- For all x > 0, let y_1(x), y_2(x), and y_3(x) be the functions satisfying dy_1 dx - ( x)^2y_1 = 0, y_1(1) = 5, dy_2 dx - (...
- _ x 0 1 - 2x 2x is
- _ x ( x^2 + 5x + 3 x^2 + x + 3 )^ 1 x
- _ x 0 x^n - [x] [x] , n N ([x] denotes greatest integer less than or equal to x)
- If f(1) = 1, f'(1) = 2, then _ x 1 f(x) - 1 x - 1 is
- I_n = _0^ /4 ^nx ,dx then _ n n [I_n + I_ n-2 ] equals
- If _ x 0 (3+x) - (3-x) x = k, the value of k is
- Let f(a) = g(a) = k and their nth derivatives f^n(a), g^n(a) exist and are not equal for some n. Further if _ x a f(a)g(x) - f(a)...
- _ x 2 [1 - ( x 2 ) ][1 - x] [1 + ( x 2 ) ][ - 2x^3] is
- The value of _ x 0 _0^ x^2 ^2t ,dt x x is
- If _ x (1 + a x + b x^2 )^ 2x = e^2, then the values of a and b, are
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration