Question

Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x) : (cos(12x) - cos(3x))/x^2 We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2 Start by calculating the values of the function for the inputs listed in this table. x fx 0.2 24.987664 0.1 -98.998848 0.05 -19.923683 0.01 -99.853172 0.001 -998.62855 0.0001 -9989.29525 0.00001 -99862.9534' Based on the values in this table, it appears : lim x=0 from (cos(12x) - cos(3x))/x^2=

my answers don’t match when I put in calculator the cos of any x value

Answer 1

Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Explanation: