2.66 Let fn(x) = z for all r E R. a) Find the pointwise limit of fn. b) Does f converge uniformly on R? Prove vour conclusion,

A:

A: To prove thatlimn→∞​yn​−xn​f(yn​)−f(xn​)​=f′(c)given that  f(x)  is differentiable at  c , we follow…

A:

A:

A: If each ,  is continuous and pointwise convergent on D and the sum function f of the sequence is…

A:

A: Step 1: Explanation for question

A: Given function is g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even.

A:

A: Given that, f is a continuous function on [0,∞). And, ∫3∞f(x)dx  converges. Then,…

A:

A: We have to give an example of a function f(x) that is not bounded on [a, b].

A: Step 1: Define the Slope: Define  m=limx→0​xf(x)​​. This gives the slope of the function near zero,…

A:

A: :

A: Letxn=1n;  yn=12n 1n-12n=2-12n=12n→0 as n→∞

A: Solution