Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0.2− 5x − 1|5x3 − x2|
Question
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0.2− 5x − 1|5x3 − x2|
Solution 1
To find the limit of the given function as x approaches 0.2, we can simply substitute 0.2 into the function because it is a continuous function at x = 0.2.
The function is: |5x^3 - x^2| - 5x - 1
Substitute x = 0.2 into the function:
= |5*(0.2)^3 - (0.2)^2| - 5*0.2 - 1 = |0.040 - 0.04| - 1 - 1 = |0| - 2 = 0 - 2 = -2
So, the limit of the function as x approaches 0.2 is -2.
Solution 2
To find the limit of the given function as x approaches 0.2, we can simply substitute 0.2 into the function because the function is continuous at x = 0.2.
The function is: |5x^3 - x^2| - 5x - 1
Substitute x = 0.2 into the function:
= |5*(0.2)^3 - (0.2)^2| - 5*0.2 - 1 = |0.040 - 0.04| - 1 - 1 = |0| - 2 = 0 - 2 = -2
So, the limit of the function as x approaches 0.2 is -2.
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