Question

Find the limit as x approaches π/2 of 3sec(x) - 3tan(x).

A) -[infinity]
B) 0
C) 3
D) Undefined

Answer 1

To find the limit as x approaches π/2 of 3sec(x) - 3tan(x), substitute trigonometric identities and simplify the expression. The limit is undefined due to a division by zero.

Step-by-step explanation:

To find the limit as x approaches π/2 of 3sec(x) - 3tan(x), we can use trigonometric identities. Recall that sec(x) is the reciprocal of cos(x) and tan(x) is the sine of x divided by the cosine of x. Substitute these identities into the expression:

limx→π/2 (3sec(x) - 3tan(x)) = limx→π/2 (3/cos(x) - 3(sin(x)/cos(x)))

Now, simplify the expression:

= limx→π/2 (3 - 3sin(x)) / cos(x)

Since the limit as x approaches π/2 of sin(x) is 1 and cos(x) is 0, the expression becomes:

= (3 - 3(1)) / 0

The expression is undefined since we have a division by zero. Therefore, the answer is option D) Undefined.