Using the limit definition, it is proved that the square of X is equal to 16 when x approaches 4

Using the limit definition, it is proved that the square of X is equal to 16 when x approaches 4

For arbitrary ε> 0
If x is limited to 0

It is proved by definition that when x approaches 2, the limit of X-2 under the root sign is equal to 0

x→2
lim √(x-2)=0
From the title, x > 2
consider
|√(x-2)-0|
=√(x-2)
=√|x-2|
To any ε> 0, take δ=ε^ 2, when 0

It is proved that the limit of (x ^ 2 + 4) / (x + 2) is - 4 when x tends to - 2

LIM (x - > - 2) (x ^ 2-4) / (x + 2) should be like this!
=lim(x->-2) (x+2)(x-2)/(x+2)
=lim(x->-2) (x-2)
=-4

Cos1 / X when x approaches 0, is there a limit, The English answer is the best

There is no limit to decisiveness. The result is infinity. Are you sure you have the right number? Or cos (1 / x). If this is the case, there is no limit

Find f (x) = x / X.G (x) = |x| / X. the left and right limits when x tends to 0, and explain whether their limits exist when x tends to 0

The left and right limits of F are equal to 1, so the existence of the limit is equal to 1
However, the left limit of G is - 1 and the right limit is 1, so the limit does not exist

F (x) = x / X is there a limit when x approaches 0

Of course, defined by the limit, the limit exists and is equal to 1