The Candy Factory sells candy by the pound, charging $1.50 per pound for quantit

Question

The Candy Factory sells candy by the pound, charging $1.50 per pound for quantities up to and including 30 pounds. Above 30 pounds, the Candy Factory charges $1.30 per pound for the entire quantity. If x represents the number of pounds, the price function is as follows. p(x) = {1.50x for x lessthanorequalto 30 1.30 x for x > 30 Find lim_x rightarrow 30^- p(x) lim_x rightarrow 30^+ p(x), and lim_x rightarrow 30 p(x) Find lim_x rightarrow 30^- p(x). Find lim_x rightarrow 30^+ p(x). Find lim_x rightarrow 30 p(x). Select the correct answer below and, if necessary, fill in the answer box to complete your choice. lim_x rightarrow 30 p(x) Type an integer or a decimal lim_x rightarrow 30 p(x) does not exist.

Explanation / Answer

here as x---30-

hence limx---30-P(x) =1.5*30 =45

also when x--30+

limx---30+P(x) =1.3*30 =39

as for a limit to exist left and right limit should be equal

therefore limx---30P(x) does not exist.

therefore option B is correct.

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