Prove the following limit. ) f(x)=x²+2x+6 where lim, 3 f (x)= 21 >) lim x – x+1=-5 =) lim x³ = 8

Q: Evaluate lim f(x), lim f(x), and lim f(x) at the point a = 5, if the limits exist. (If an answer…

A: Given function : f(x) = 10 -x  if x ≤5 f(x) = x + 3 if x > 5

Q: Find the limit of Sin Cath)-sina lim

A: we need to find the value of, limh→0sin(a+h) - sin(a)h   when we substitute h=0, sina+0 - sina0 = 00…

Q: Find the limits lim e sin -!

A: Given

Q: 6) Find the limet lim Cう(0)) メye 2. メッリ

A:

Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: How to evaluate the attached limit.

A: The given limit is,

Q: Find the limit "L" The prove how the limit is "L"

A: Given function is

Q: Prove the limit using epsilon/ delta.

A: To prove the statement by using epsilon, delta definition of a limit is,

Q: Find the limit analytically

A: Given, limit function is

Q: x³-8 4 x+2 x 16 2. lim

A:

Q: 1-cos 2x lim 4x

A:

Q: What is the Limit of identity function?

A: we have to tell what is the limit of an identity function.

Q: Evaluate the limit. lim ||A||-0 Δ ο Σ. (x - x;) Δx, where i = 1 and Ax = - 1 n where x, = an n…

A: Given,               lim∆→0∑i=1nxi2-xi7∆x,  Where xi=1n and ∆x=1n.

Q: lim, (V+x+1 - V+1) – Vx² x* + 1

A:

Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Prove that lim (4x² – 25) = -9. X→2

A: We will prove this by definition of limit as follows

Q: sin r lim ,3 81.

A:

Q: what epsilon and delta mean in the epsilon‐delta definition of the limit.

A:

Q: Prove that lim n! n n = 0

A: lim fn=limn!nn We know that hlim gx=limfgx Therefore loglimfn=limlogn!nn…