Pls Answer the question attached!!! Problem 1: Continuity and differentiabilitya)Use either numerical or graphical methods (utilise Excel spreadsheets or Desmos) to estimatelimits for each of the following functions. Give your answers accurate to 2 decimal places.lim(1 +x)iv.lim |x|i.2x + 3,x + -11limlim f(x) = {"4,11.V.x-1X = -1x-1x-1limvi.lim sin-111.b)Using the relations above as examples, discuss whether or not limits always exist. If yes,prove your answer. If no, summarise the characteristics of relations when their limits do notexist.c)Decide whether or not each of the relations above is continuous at the given point and givereasons to your answers (refer to the definition of continuity).d)Discuss how continuity of a relation affects the existence of its limit.e)Decide whether or not each of the relations above is differentiable at the given point (refer tothe definition of differentiability).f)Discuss if there is any relationship between the continuity and differentiability of a relation ata given point.

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Description: Pls Answer the question attached!!! Problem 1: Continuity and differentiabilitya)Use either numerical or graphical methods (utilise Excel spreadsheets or Desmos) to estimatelimits for each of the following functions. Give your answers accurate to 2 d

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Answered: i. lim(1 + x)5

Calculus: Early Transcendentals

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ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Pls Answer the question attached!!!

Problem 1: Continuity and differentiability
a)
Use either numerical or graphical methods (utilise Excel spreadsheets or Desmos) to estimate
limits for each of the following functions. Give your answers accurate to 2 decimal places.
lim(1 +x)
iv.
lim |x|
i.
2x + 3,
x + -1
1
lim
lim f(x) = {"
4,
11.
V.
x-1
X = -1
x-1x-1
lim
vi.
lim sin-
111.
b)
Using the relations above as examples, discuss whether or not limits always exist. If yes,
prove your answer. If no, summarise the characteristics of relations when their limits do not
exist.
c)
Decide whether or not each of the relations above is continuous at the given point and give
reasons to your answers (refer to the definition of continuity).
d)
Discuss how continuity of a relation affects the existence of its limit.
e)
Decide whether or not each of the relations above is differentiable at the given point (refer to
the definition of differentiability).
f)
Discuss if there is any relationship between the continuity and differentiability of a relation at
a given point.

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