Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f : (0, π) → ℝ be a function given by f(x) = cases ( 87 )^ 8x 7x , & 0 < x < 2 a - 8, & x = 2 (1 + | x|)^ ba| x| , & 2 < x <...
- Consider the function. f(x) = cases a(7x-12-x^2) b|x^2-7x+12| , & x<3 [2mm] 2^ (x-3) x-[x] , & x>3 [2mm] b, & x=3 cases Where [x]...
- Let f(x) = _ r x 2r^2[(f(r))^2 - f(x)f(r)] r^2 - x^2 - r^3e^ f(r) r be differentiable in (−∞, 0) ∪ (0, ∞) and f(1) = 1. Then the...
- Consider the function f : [1/2, 1] → ℝ defined by f(x) = 4√2x³ – 3√2x – 1. Consider the statements (I) The curve y = f(x)...
- Let a and b be real constants such that the function f defined by f(x) = cases x^2 + 3x + a, & x 1 bx + 2, & x > 1 cases be...
- If the function f(x) = cases 1 |x| , & |x| 2 ax^2 + 2b, & |x| < 2 cases is differentiable on ℝ, then 48(a + b) is equal to...
- Consider the function f : (0, ∞) → ℝ defined by f(x) = e^ -| _ex| . If m and n be respectively the number of points at which f is...
- Let g(x) be a linear function and f(x) = cases g(x), & x 0 ( 1+x 2+x )^ 1/x , & x > 0 cases , is continuous at x = 0. If f′(1) =...
- Let [t] denote the greatest integer t. The number of points where the function f(x)=[x]|x^2-1|+ ( [x]+3 )-[x+1], x (–2,2) is not...
- Let R be such that the function f(x)= cases ^ -1 (1- x ^2) ^ -1 (1- x ) x - x ^3 , & x 0 , & x=0 cases is continuous at x = 0,...
- Let f : R R and g : R R be defined as f(x)= cases x+a, & x<0 |x-1|, & x 0 cases and g(x)= cases x+1, & x<0 (x-1)^2+b, & x 0 cases...
- Let the functions F:R R and g:R R be defined as : f(x)= cases x+2, & x<0 ^2, & x 0 cases , g(x)= cases x^3, & x<1 3x-2, & x 1...
- If the function f(x) = ( x)- x x^4 is continuous at each point in its domain and f(0) = 1 k , then k is ——
- Let f : R R be a function defined as f(x)= cases (a+1)x+ 2x 2x , & x<0 , & x=0 x+bx^3 - x bx^ 5/2 , & x>0 cases . If f is...
- If f(x)= cases 1 |x| , & |x| 1 ^2+b, & |x|<1 cases is differentiable at every point of the domain, then the values of a and b are...
- Let a function g : [0, 4] R be defined as g(x)= cases _ 0 t x t^3-6t^2+9t-3 , & 0 x 3 4-x, & 3<x 4 cases then the number of...
- Let a function f : R R be defined as f(x)= cases x-e^x, & x 0 +[-x], & 0<x<1 2x-b, & x 1 cases where [x] is the greatest integer...
- Let f : R R be defined as f(x)= cases x^3 (1- 2x)^2 _e ( 1+2xe^ -2x (1-xe^ -x )^2 ), & x 0 , & x=0 cases If f is continuous at x...
- Let f : R R be a function defined as f(x)= cases 3 (1- |x| 2 ), & |x| 2 0, & |x|>2 cases Let g : R be given by g(x) = f(x + 2) –...
- If f:R R is a function defined by f(x)=[x-1] ( 2x-1 2 ) , where [.] denotes the greatest integer function, then f is :
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