Sets And Functions Multiple Choice Questions & Answers

If β=1 then f is differentiable

If β>0 then f is uniform continuous

If β>1  then f is constant function

F must be a polynomial

F ^-1 (G ₁ ∪ G ₂ )= f ^-1 ( G ₁ )∪ f ^-1 ( G ₂ )

F -1 ( G 1) c = (f -1 ( G 1 )) c

F (G 1 ∩ G 2) =f (G 1 ) ∩ f ( G 2 )

If G₁ is open and G₂ is closed then G₁+ G₂ = {x+y : x∈ G₁,y∈ G₂ is neither open nor closed

  (1+ 1 /n) ^{n +1} → e   as n →∞

(1+ 1 /n+1 )ⁿ →e  as n→∞ 

(1+ 1 /n )^{n 2} →e  as n→∞ 

(1+ 1 /n ²) ⁿ →e  as n→∞ 

{x₁,x₂,x₃,……….x_n   : x_i<1,   1≤i≤n}  

{x ₁ , x ₂ , x ₃ ,………. x _n   : x ₁ + x ₂ + x ₃ ……. x _n =0}

{x ₁ , x ₂ , x ₃ ,………. x _n : x _i ≥0,  1≤i≤n}

{x ₁ , x ₂ , x ₃ ,………. x _n :   1≤x _i ≤2,  1≤i≤n }

X cannot be compact

X contains an interior point

X may be closed

Closure of X is countable

{(x,y):  |x|≤5 , |y|≤10}

{(x,y) :   x ² + y ² =1} 

{(x,y) :  y ≥ x ² }

{(x,y) :  y≤ x ^2 }

0 is an isolated point.

(–2, 0] is an open set

0 is a limit point of the subset {1 /n ,n∈N}

(–2, 0) is an open set

Discontinuous somewhere

Continuous on R but differentiable only at x=1

Continuous on R but differentiable only at x=1,2

Continuous on R but not differentiable only at   x=1, 3/ 2 ,2

The closure of the interior of A

A countable set

A compact set

Not open