The function $f ( x ) = 9 - 2 x + x ^ { 2 }$ is both continuous and differentiable at $x = 0$ Write these facts as limit statements.

Name: The function $f ( x ) = 9 - 2 x + x ^ { 2 }$ is both continuous and differentiable at $x = 0$ Write these facts as limit statements.
Brand: Quizplus
Rating: 4.7 (28 reviews)

Question

Quizplus · Accepted Answer

The Answer is Since f is continuous at x = 0,

\lim _ { x \rightarrow 0 } \left( 9 - 2 x + x ^ { 2 } \right) = f ( 0 ) = 9

Since f is differentiable at x = 0,

\lim _ { h \rightarrow 0 } \frac { - 2 h + 2 x h + h ^ { 2 } } { h }

exists.
Note that there are alternate ways of writing the answer

The Function f(x)=9−2x+x2f ( x ) = 9 - 2 x + x ^ { 2 }f(x)=9−2x+x2

The Function $f ( x ) = 9 - 2 x + x ^ { 2 }$