need answer in details. You will get like on Providing all Parts of this Question. i.e Q1 Transcribed Image Text: 1 Let (an) be a sequence of real numbers.

Using the definition of the limit of a sequence, prove the following results.

(a) lim

n+0 n2 + 3n +4

5n2 – 7n sin n

= 5.

(b) If lim a,, = L> 0. then there exists an integer N such that

%3D

4.

an >L,

for all n N.

(c) If lim an =

L and lim b, =

M then lim anb, = LM.

%3D Transcribed Image Text: If a question says to ‘use the definition’ to prove some result, your answer must rely solely on the

definition to prove the result, and not on other results from the course.

If the question does not say this then you may use any result from the course in your answer.