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Tcecarenko [31]
3 years ago
12

on january 1,1999,the price of gasoline was$1.39 per gallon .if the price of gasoline increased by 0.5%per month ,what was the w

as the cost of one gallon of gasoline,to the nearest cent,on january 1 one year later?
Mathematics
1 answer:
arlik [135]3 years ago
4 0
P(t)=1.39.(1.005)^t \ \ \ \ where t \ is \ time \ in \ months\\
\\
P(1)=1.39.(1.005)^1\\
\\
P(1)=1.39*1.005\\
\\
P(1)=\$ \ 1.40
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Find the indicated limit, if it exists.
kondor19780726 [428]

Answer:

d) The limit does not exist

General Formulas and Concepts:

<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Property [Addition/Subtraction]:                                                                   \displaystyle \lim_{x \to c} [f(x) \pm g(x)] =  \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}

<u>Step 2: Find Right-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} 5 - x = 5 - 5 = 0

<u>Step 3: Find Left-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^-} x + 3
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} x + 3 = 5 + 3 = 8

∴ Since  \displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)  , then  \displaystyle \lim_{x \to 5} f(x) = DNE

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

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Hi,
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6 0
3 years ago
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8 0
3 years ago
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Answer:

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Now: 1 mm

In 10 minutes: 3 * 1 mm = 3 mm

In 20 minutes: 3 * 3 mm = 9 mm

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