How can you tell if a discontinuity of a limit is removable or not removable?

Mathematics

1 answer:

azamat2 years ago

8 0

A discontinuity is present if any of ...

the limit doesn't exist
the limit is not the same as the value of the function

If the one of these that is the cause of discontinuity is the last one and defining the function will make this issue go away, then the discontinuity is removable.

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Please help me with question 3

zzz [600]

My gut tells me its C

5 0

3 years ago

Need help with number 3 inequalities with variables on both sides

Volgvan

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

$\displaystyle{2x-3 \leq \dfrac{x}{2}}$

First, get rid of the denominator by multiplying both sides by 2:

$\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}$

Add both sides by 6 then subtract both sides by x:

$\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}$