Question

Evaluate this limit:

Answer 1

\[\lim_{x \rightarrow 2} \frac{ 4-x^2 }{ 2-x }\]

Answer 2

Hint: It's an indeterminate form.

Answer 3

i know it's 0/0 but i don't know what to do next

Answer 4

You also have difference of squares!

Answer 5

\[(a^2-b^2)=(a-b)(a+b)\]

Answer 6

We calculate the limit substituting x by 2

lim (4 - x^2 )/(2-x) = (4-4)/(2-2) = 0/0

We could write the numerator as a difference of squares:

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

lim (4 - x^2)/(2-x) = lim (2 - x)(2 + x)/(2-x)

We'll simplify and we'll get:

lim (2+x) = 4

Answer 7

anyway u may use derivative
derivative of 4-x^2 is -2x
and derivative of 2-x is -1
so, just plug in x=2 to (-2x)/-1 = 4