A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour (A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

The piece wise definition of the cost for a month in which a member uses a car for hours is given by the equation,.

Given,

Membership plan is per month.

We have to write a piece wise definition of the cost for a month in which a member uses a car for hours.

Here, per month fees includes 10 hours of driving each month, so the cost for a month is given as,

Here is the no. of additional hours for the month.

Further,

.

Now at,

Or,

Similarly, at left limit,

Or,

Finally at ,

Since

So the required function is discontinuous at

Hence the piece wise definition of the cost for a month in which a member uses a car for hours is given by the equation,.

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Answer and Step-by-step explanation:

Given:

Charges includes 10 hour per month = $50

Charges for additional hour = $9

Piecewise definition of cost F(x) for a month in which a member use a car for  hours.

Find limits?

Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Lim x → 10- F(x) = 50$

Lim x → 10 [ 9x – 70] = 9( 10) – 70  

                                = 90 – 70

                                = 20 > 10

Limit does not exist.

Lim x → 10+ F(x) = 50$

Lim x → 10+  F(x) = Lim x → 10+   [90x – 70]

                         = 90 – 70

                          = 20 > 10

Limit does not exist.

Lim x → 10 F(x) = 50$

An integer or an decimal.

The limit does not exist.

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