Continuity and Differentiability questions
732 published questions with worked solutions.
- If f : R R given by f(x) = cases 2 x, & if x - 2 a x + b, & if - 2 < x < 2 1 + ^2 x, & if x 2 cases is a continuous function on...
- If the function f(x) = cases x^2 - (k + 2)x + 2k x - 2 , & for x 2 [1mm] 2, & for x = 2 cases is continuous at x = 2, then k is...
- If the function f(x) = cases x, & if x 1 cx + k, & if 1 < x < 4 -2x, & if x 4 cases is continuous everywhere, then the values of...
- If f(x) = cases 3 x 5x , & x 0 [1mm] 2k, & x = 0 cases is continuous at x = 0, then the value of k is equal to
- If f(x) = cases ax + 3, & x 2 a^2x - 1, & x > 2 cases , then the values of a for which f is continuous for all x are
- Which of the following function is not continuous at x = 0?
- If the function f(x) = (1 + ax) - (1 - bx) x , x 0 is contintious at x = 0, then
- If f(x) = cases x^2 + , & x 0 2 x^2 + 1 + , & x < 0 cases is continuous at x = 0 and f ( 1 2 ) = 2, then ^2 + ^2 is
- If f(x) = e^ x^2 - x x^2 , for x 0 is continuous at x = 0, then value of f(0) is
- If the function f(x) = [ ( 4 + x ) ]^ 1 x for x 0 is continuous at x = 0, then f(0) =
- Consider the following in respect of the function f(x)= cases 2+x, & x 0 2-x, & x<0 cases 1. _ x 1 f(x) does not exist. 2. f(x)...
- Let f : A R where A= R 0 is such that f(x)= x+|x| x . On which one of the following sets is f(x) continuous?
- Let f(x) be defined as follows : f(x)= cases 2x+1, & -3<x<-2 -1, & -2 x<0 +2, & 0 x<1 cases Which one of the following statements...
- Suppose the function f(x)=x^n, n 0 is differentiable for all x. Then n can be any element of the interval
- A function is defined as follows : f(x)= cases - x x^2 , & x 0 0, & x=0 cases Which one of the following is correct in respect of...
- Consider the following : 1. x+x^2 is continuous at x=0 2. x+ 1 x is discontinuous at x=0 3. x^2+ 1 x is continuous at x=0 Which...
- A function is defined in (0, ) by f(x)= cases 1-x^2 & for 0<x 1 x & for 1<x 2 2-1+0 5x & for 2<x< cases Which one of the...
- Consider the following statements : 1. Derivative of f(x) may not exist at some point. 2. Derivative of f(x) may exist finitely...
- The left-hand derivative of f(x)=[x] ( x) at x=k where k is an integer and [x] is the greatest integer function, is
- If f(x)= x 2 -1, then on the interval [0, ] which one of the following is correct?
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