Question

Which statement about the limit expression limx→0 tan(x)/2x is not correct?

a) The limit does not exist.
b) The limit is 1/2.
c) The limit is 0.
d) The limit is [infinity].

Answer 1

The incorrect statement about the limit of tan(x)/2x as x approaches 0 is that the limit is 0. The actual limit, using the standard limit of sin(x)/x, is 1/2.

Step-by-step explanation:

The question is asking about the limit of the expression tan(x)/2x as x approaches 0. We can evaluate this limit by recognizing a standard limit in calculus, which is limx→0 (sin x) / x = 1. The tangent function can be written as sin(x)/cos(x), so our limit becomes (sin(x)/cos(x))/(2x). Since cos(0) = 1, we can simplify our limit to limx→0 (sin x) / (2x * cos x). If we separate the sine and cosine, we have (1/cos x) * (sin x / (2x)). Since the limit of sin(x)/x as x approaches 0 is 1 and cos(0) is 1, our new expression becomes 1 * 1/2, therefore the limit is 1/2.