Consider the functions given by $$f ( x ) = 2 \sin x$$
$$and$$
$$g ( x ) = \frac { 1 } { 2 } \csc x$$ on the interval (0,π). Describe the behavior of each of the functions as x approaches π.

A)f approaches 2 and g approaches +∞.
B)f approaches 0 and g approaches +∞.
C)f approaches +∞ and g approaches 0.
D)f approaches 0 and g approaches $$\frac { 1 } { 2 }$$ .
E)f approaches 2 and g approaches $$\frac { 1 } { 2 }$$ .

Question

Consider the functions given by​ $$f ( x ) = 2 \sin x$$
$$and$$
$$g ( x ) = \frac { 1 } { 2 } \csc x$$ on the interval (0,π). Describe the behavior of each of the functions as x approaches π.
​
A)f approaches 2 and g approaches +∞.
B)f approaches 0 and g approaches +∞.
C)f approaches +∞ and g approaches 0.
D)f approaches 0 and g approaches $$\frac { 1 } { 2 }$$ .
E)f approaches 2 and g approaches $$\frac { 1 } { 2 }$$ .

Quizplus · Accepted Answer

As x approaches π, the cosine function in f(x) approaches -1, while the sine function in g(x) approaches 0. Therefore f(x) approaches 0, and g(x) approaches +∞. Thus, the correct choice is B.

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Consider the Functions Given By $f ( x ) = 2 \sin x$