Mathematics: Can someone help me figure out what this is?

Can someone help me figure out what this is?

10040813

26.01.2022

1.9

Step-by-step explanation:

pi = 180 degrees

pi/3 = 180/3

degree = 60

60/360 = 6

circumference: 2*6 = 12

12/pi = 3.81971863421

ans/2 = 1.90985931711

round: 1.9

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yrkfred1440

05.03.2020

$\displaystyle\lim_{x\to2}\frac{x^2+4x-12}{x-2}$

Substituting x=2

directly yields $\dfrac{4+8-12}{2-2}=\dfrac00$ . Applying L'Hopital's rule, we have

$\displaystyle\lim_{x\to2}\frac{2x+4}1=4+4=8$

But note that x-2

is a factor of the numerator, which follows from the remainder theorem: if x=2

, then

which means x-2

is a factor of the numerator.

We have

x^2+4x-12=(x-2)(x+6)

and so

$\displaystyle\lim_{x\to2}\frac{x^2+4x-12}{x-2}=\lim_{x\to2}\frac{(x-2)(x+6)}{x-2}=\lim_{x\to2}(x+6)=2+6=8$

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