10. Define fnil0, 00) → R by sin (nx) fn (x) = 1+nx a) Show that fr converges pointwise on [0,00)and find the point wise limit f. b) Show that fn → f uniformly on [a, c0)for every a > 0 c) Show that fn→ f uniformly on [a, )for every [0,00)

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10. Define fn:l0, 00) → R by
sin (nx)
fn (x)
1+nx
a) Show that fn converges pointwise on [0,00)and find the point wise limit f.
b) Show that fn → f uniformly on [a, co0)for every a > 0
c) Show that fn → f uniformly on [a, co)for every [0,c0)
Transcribed Image Text:10. Define fn:l0, 00) → R by sin (nx) fn (x) 1+nx a) Show that fn converges pointwise on [0,00)and find the point wise limit f. b) Show that fn → f uniformly on [a, co0)for every a > 0 c) Show that fn → f uniformly on [a, co)for every [0,c0)
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