Brief calculus.

Question

1. Consider the graph of f(x)

Find the following limits, use approximate values when necessary:

a) lim_x→3⁺ f (x) =

b) lim_x→ 3^- f (x) =

c) lim_{x→ 3} f (x) =

d) lim_x→-2^- f (x) =

e) lim_{x→ -2}⁺ f (x) =

f) lim_{x→ -2} f (x) =

g) lim_x→1 f (x) =

h) lim_x→-oo f (x) =

i) lim _{x→ oo f (x) =}

https://drive.google.com/file/d/1AWLPzEd3V_BZBMDmhvSItRb0wewXr8sh/view?usp=sharing

this link is for the graph.

Answer 1

a) -4

b) 2

c) Does Not Exist

d) -2

e) -2

f) -2

g) 3

h) Infinity

i) Infinity

The limit does not exist at 3 because the limit from the left and the right are different values. In contrast, the limit at -2 does exist because the left and the right approach the same value despite the hole. For limits at negative infinity and positive infinity just look at the arrow direction on the left-most and right-most side.