Learn more about our help with Assignments: Math
Search & Filtering
Show that the sequence (f) where f(x)= x/(1+2nx^2), x∈ [1,∞[ is uniformaly convergent in [1,∞[
Check whether the function f (x) = [x]+ e^x is integrable in [0,3].
Evaluate the limit as n → ∞ of the sum
1/n [sin (π/n) +sin (2π)/n +.....+ sin (2nπ)/n]
1/n [sin (π/n) +sin (2π)/n +.....+ sin (2nπ)/n]
Show that the function f :[0, 1] → R defined by
f(x)= { 1, when x is rational ; 2 when x is irrational
is not Riemann integrable.
f(x)= { 1, when x is rational ; 2 when x is irrational
is not Riemann integrable.
Show that the function f defined on R by
f(x)={3x^(2) cos(1)/(2x), when x≠0 ; 0, when x=0
is derivable on R but f ′ is not continuous at x=0
f(x)={3x^(2) cos(1)/(2x), when x≠0 ; 0, when x=0
is derivable on R but f ′ is not continuous at x=0
Show that the set B = {x | x^(2) > 2} is non-empty and bounded below. Is it bounded
above? Justify.
above? Justify.
Evaluate: lim x→∞ {[2x^(2) +3x-2]^(1/2)}-{[2x^(2) -3x+2]^(1/2)}
Check whether the following sequences{sn} are Cauchy, where
(i) sn = 1+2+3+....+n
(ii) sn = [4n^(3)+3n]/[3n^(3)+n^(2)]
(i) sn = 1+2+3+....+n
(ii) sn = [4n^(3)+3n]/[3n^(3)+n^(2)]
For the following sequences, find two subsequences which are convergent:
(i) a(subscript n)= n[1+(-1)^n]
(ii) a(subscript n)= sin [(nπ)/3]
(i) a(subscript n)= n[1+(-1)^n]
(ii) a(subscript n)= sin [(nπ)/3]
Show that the function f given by
f(x)=1/[x+2]^3 ∀x∈]-2,2[
is continuous but not bounded in ]− 2, 2 [
f(x)=1/[x+2]^3 ∀x∈]-2,2[
is continuous but not bounded in ]− 2, 2 [
