Question

In exercises 31 and 32, how do you find all points of discontinuity of the function?

a) By analyzing the limits at specific values
b) By finding the roots of the function
c) By computing the derivative of the function
d) By using the intermediate value theorem

Answer 1

To find all points of discontinuity of a function, we analyze the limits at specific values. By evaluating the limits at different values, we can identify where the function is discontinuous. Hence the correct answer is option A

Step-by-step explanation:

To find all points of discontinuity of a function, we need to analyze the limits at specific values. This is option a) in the question. A point of discontinuity occurs when the limit at a specific value does not exist or is different from the function's value at that point. By evaluating the limits at different values, we can identify where the function is discontinuous.

For example, if we have the function f(x) = 1/x, we can analyze the limit as x approaches 0. The limit does not exist because the function approaches positive infinity from the right side of 0 and negative infinity from the left side of 0. Therefore, 0 is a point of discontinuity for this function.

So, the correct answer to the question is a) By analyzing the limits at specific values.