Information about a function near is given below

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Information about a function

h

near

x=4

is given below. For

x<4

: x : 3.9 3.99 3.999 h(x): 2.05 2.005 2.0005 For

x>4

: x : 4.001 4.01 4.1 h(x): 1.9995 1.995 1.95 The value at the point is

h(4)=3

. Which one of the following statements is correct? (a)

\displaystyle \lim_{x\to4}h(x)=3

(b)

\displaystyle \lim_{x\to4}h(x)\text{ does not exist}

(c)

\displaystyle \lim_{x\to4}h(x)=2

and this limit equals

h(4)

(d)

\displaystyle \lim_{x\to4}h(x)=2

but this limit is not equal to

h(4)