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The local gas company uses the following function for computing their customers' monthly gas bills.C(x)={0.5x+8.839.35x−2646.17if0<x≤300ifx>300𝐶(𝑥)={0.5𝑥+8.83if0<𝑥≤3009.35𝑥−2646.17if𝑥>300, where x is the number of therms (thermal units) used and C(x)𝐶(𝑥) is the cost in dollars.Step 1 of 3 :  Find limx→300−C(x)lim𝑥→300−⁡𝐶(𝑥).

Question

The local gas company uses the following function for computing their customers' monthly gas bills.C(x)={0.5x+8.839.35x−2646.17if0<x≤300ifx>300𝐶(𝑥)={0.5𝑥+8.83if0<𝑥≤3009.35𝑥−2646.17if𝑥>300, where x is the number of therms (thermal units) used and C(x)𝐶(𝑥) is the cost in dollars.Step 1 of 3 :  Find limx→300−C(x)lim𝑥→300−⁡𝐶(𝑥).

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Solution

To find the limit of the function C(x) as x approaches 300 from the left (denoted as lim(x→300-) we use the first piece of the piecewise function, as this piece is valid for x values less than or equal to 300.

The first piece of the function is C(x) = 0.5x + 8.83.

Substitute x = 300 into this function:

C(300) = 0.5(300) + 8.83 = 150 + 8.83 = 158.83

So, lim(x→300-)C(x) = 158.83.

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