Describe the behavior of the function as $x$ approaches zero.
$f ( x ) = 2 x \sin x ^ { 2 }$
A) $f \rightarrow 0$ as $x \rightarrow 0$.
B) $f \rightarrow - 1$ as $x \rightarrow 0$.
C) $f \rightarrow 1$ as $x \rightarrow 0$.
D) $f \rightarrow - \infty$ as $x \rightarrow 0$.
E) $f \rightarrow + \infty$ as $x \rightarrow 0$.

Question

Describe the behavior of the function as $x$ approaches zero. 
$f ( x ) = 2 x \sin x ^ { 2 }$
A) $f \rightarrow 0$ as $x \rightarrow 0$.
B) $f \rightarrow - 1$ as $x \rightarrow 0$.
C) $f \rightarrow 1$ as $x \rightarrow 0$.
D) $f \rightarrow - \infty$ as $x \rightarrow 0$.
E) $f \rightarrow + \infty$ as $x \rightarrow 0$.

Quizplus · Accepted Answer

As $x$ approaches zero, the function behaves like $2x\cdot1(\text{since } \sin(0)=0)$, which approaches zero as $x$ approaches zero. Thus, $f\rightarrow0$ as $x\rightarrow0$.

Describe the Behavior of the Function As xxx Approaches Zero f(x)=2xsin⁡x2f ( x ) = 2 x \sin x ^ { 2 }f(x)=2xsinx2

Describe the Behavior of the Function As $x$ Approaches Zero $f ( x ) = 2 x \sin x ^ { 2 }$