During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new salesperson depend on the number of hours x of training, as follows.S = S(x) = 7x + 14 + x2,    x ≥ 2(a) Findlim x→2+ S(x).thousands of dollars (b) Findlim x→14 S(x).thousands of dollars

Question
Asked Jun 15, 2019

During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new salesperson depend on the number of hours x of training, as follows.

S = S(x) = 
7
x
 + 14 + 
x
2
,    x ≥ 2
(a) Find
lim x→2+ S(x).

thousands of dollars

(b) Find
lim x→14 S(x).

thousands of dollars
check_circleExpert Solution
Step 1

During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new salesperson depend on the number of hours x of training, as follows.

S(x)= 7x +14 x2
= x 7x 14
...1)
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S(x)= 7x +14 x2 = x 7x 14 ...1)

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Step 2

In order to find lim x→2+ S(x).

Substitute 2+h for x in equation 1.

lim(2+h)(2+) +7(2+h)+14
h-0
=4 4h h14+7h+14
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lim(2+h)(2+) +7(2+h)+14 h-0 =4 4h h14+7h+14

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Step 3

Substitute 0 for h in ...

4+4(0)+(0)4+7(0)+14 4+14+14
- 32
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4+4(0)+(0)4+7(0)+14 4+14+14 - 32

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Calculus