Question

What is the limit of (x cot(theta) - theta cot(x))/(x - theta) as x approaches theta?

A) 0
B) 1
C) -1
D) cot(theta)
E) csc(theta)

Answer 1

The limit of the given expression does not match any of the provided options.

Step-by-step explanation:

To find the limit of the given expression as x approaches theta, let's simplify it:

Using the identity cot(theta) = 1/tan(theta), we can rewrite the expression as:

(x/tan(theta) - theta/tan(x))/(x - theta)

Since cot(theta) = 1/tan(theta), this can be further simplified to:

(x/tan(theta) - theta/tan(x))/(x - theta) = (x - theta)/(x*tan(theta) - theta*tan(x))

Now, as x approaches theta, both x and theta approach the same value. Therefore, the denominator approaches 0, resulting in the limit approaching infinity. Hence, the answer is not one of the given options.