lim f(x)=4 and lim f(x)=4, but f(6)= -4.\n x→6^- x→6^+\n what can you say about lim f(x)?\n x→6\n lim f(x)\n…

lim f(x)=4 and lim f(x)=4, but f(6)= -4.\n x→6^- x→6^+\n what can you say about lim f(x)?\n x→6\n lim f(x)\n x→6\n ○a. is ∞\n ○b. is 4\n ○c. is -4\n ○d. does not exist

lim f(x)=4 and lim f(x)=4, but f(6)= -4.\n x→6^- x→6^+\n what can you say about lim f(x)?\n x→6\n lim f(x)\n x→6\n ○a. is ∞\n ○b. is 4\n ○c. is -4\n ○d. does not exist

Answer

Explanation:

Step1: Recall the limit existence theorem

The limit of a function ( \lim_{x\rightarrow a}f(x) ) exists if and only if ( \lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x) ).

Step2: Apply the theorem to the given problem

Here ( a = 6 ), ( \lim_{x\rightarrow 6^{-}}f(x)=4 ) and ( \lim_{x\rightarrow 6^{+}}f(x)=4 ). Since ( \lim_{x\rightarrow 6^{-}}f(x)=\lim_{x\rightarrow 6^{+}}f(x) = 4 ), by the limit existence theorem, ( \lim_{x\rightarrow 6}f(x) ) exists. The value of the function ( f(6)=-4 ) does not affect the limit value. The limit as ( x ) approaches ( 6 ) depends on the behavior of the function near ( x = 6 ), not the value of the function at ( x = 6 ).

Answer:

B. is 4