How do you go about finding limits in absolute values?

Answer by  therealscl (59)

When given an absolute value function f(x) we are asked to find lim as x->a of f(x). The standard form for an absolute value function is f(x)=a|bx+c|+d. We begin by computing the limits from the left and right of a. In other words, as the graph approaches f(a) from the left, what y-value is it? Repeat for right of a

Answer by  Yimocool (16)

One way is simply to use a device to evaluate it for you. If evaluating by hand, you express the absolute value as a piecewise function. When there is a non-removable discontinuity at that point in the graph, there is no limit.

Answer by  robin99 (17)

Absolute Value: Sometimes we need to use only positive numbers, and the absolute value is a useful tool for this purpose. When you see an absolute value in a problem or equation, it means that whatever is inside the absolute value is always positive. Absolute values are often used in problems involving distance and are sometimes used with inequalities.

Answer by  john11 (617)

If the function is continuous then the limit is unique regardless if it is an absolute value (it isn't necessarily differentiable at every point however).To find the limit of lim x->0 for y=abs(x), the answer is 0. But, since the graph changes instantly here, the derivative is not unique.

Answer by  njanetos (69)

If the limit exists, then it converges to a positive or negative number. Therefore, after a certain point in a sequence of numbers the absolute value sign does not matter. In other words, the limit of the absolute value is the absolute value of the limit.

Answer by  PowerIsMe (844)

One way to approach this would be to split up the absolute value. (Write it as -x if its <0 and x if its more than 0). Take the limit in both cases and compare.

Answer by  VB (361)

If you are trying to determine the limit of a function that involves absolute values, the easiest thing to do is to switch the order. (ie. limit(abs(something)) = abs(limit(something)) ) Since absolute values are continuous functions, it is okay to switch the order. So, find the limit first and then take the absolute value.

Answer by  njanetos (69)

Finding limits in absolute values is exactly the same as finding regular limits. To find it, simply find the limit of the sequence with the absolute values removed. Then if the limit is negative, make it positive.