Create two different functions for which the left-hand limit at zero is 0 and for which the right hand limit at zero is 8
a different problem was recently posted here where the left limit is 2 and the right limit is zero. Tweaking it a bit, we have
(8)/(1-2^(-1/x))
which fits your criteria.
If you can come up with any function where the left and right limits for some value of x are different, you can tweak it into another one which fits the criteria.
I still don't understand
lim X->0= (0)/(1+8^(1/x)
as x-> 0, 1/x -> ∞
2^(-1/x) -> 2^-∞ = 0 when x>0
2^(-1/x) -> 2^∞ = ∞ when x<0
So, in those two cases, we have
lim x->0+ = 8/(1-2^-∞) = 8/(1-0) = 8
lim x->0- = 8/(1-2^∞) = 8/-∞ = 0
http://www.wolframalpha.com/input/?i=%288%29%2F%281-2^%28-1%2Fx%29%29
I am sorry i typed the problem wrong. It says Create two different functions for which the left-hand limit at zero is 0 and for which the right hand limit at zero is negative 8
well, since -0 = 0 and -8 = -(8), it should not be hard to make the required change to the function I provided.
I mean, you do remember your basic algebra, right?
Sure! Here are two different functions that meet the criteria:
1. Function 1: f(x) = x^2
To find the left-hand limit at zero for this function, we substitute values of x that are approaching zero from the left side. As x approaches zero from the left side, the function values get closer and closer to zero.
To find the right-hand limit at zero for this function, we substitute values of x that are approaching zero from the right side. As x approaches zero from the right side, the function values get closer and closer to zero as well.
2. Function 2: f(x) = 8 for x > 0, and f(x) = 0 for x ≤ 0
In this function, the left-hand limit at zero is 0 because as x approaches zero from the left side, the function values are all 0 since f(x) = 0 for x ≤ 0.
On the other hand, the right-hand limit at zero is 8 because as x approaches zero from the right side, the function values are 8 since f(x) = 8 for x > 0.
These are two examples of functions that have different left-hand and right-hand limits at zero.