Question

How to find the limit of cos(x)/x?
a) 0
b) 1
c) -1
d) Does not exist

Answer 1

The limit of cos(x)/x as x approaches 0 does not exist since division by zero is undefined in mathematics.

Step-by-step explanation:

To find the limit of cos(x)/x as x approaches 0, we can apply L'Hôpital's rule. This rule states that if the limit of the functions in the numerator and denominator individually approach 0 or ±∞, the overall limit can be found by differentiating both the numerator and the denominator and taking the limit of that function. However, in this case, as x approaches 0, cos(x) approaches 1, but 0 in the denominator indicates a potential for an undefined expression. Therefore, the limit does not exist in the standard sense because we cannot divide by zero (x).