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Law Incorporation [45]
3 years ago
6

Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '[infinity]' or

'-[infinity]', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x→3 f(x),
where f(x) = 9 − 3x if x < 3 ;

and x^2 − x if x ≥ 3
Mathematics
1 answer:
soldi70 [24.7K]3 years ago
8 0

Answer:

The limit of this function does not exist.

Step-by-step explanation:

\lim_{x \to 3} f(x)

f(x)=\left \{ {{9-3x} \quad if \>{x \>< \>3} \atop {x^{2}-x }\quad if \>{x\ \geq \>3 }} \right.

To find the limit of this function you always need to evaluate the one-sided limits. In mathematical language the limit exists if

\lim_{x \to a^{-}} f(x) = \lim_{x \to a^{+}} f(x) =L

and the limit does not exist if

\lim_{x \to a^{-}} f(x) \neq \lim_{x \to a^{+}} f(x)

Evaluate the one-sided limits.

The left-hand limit

\lim_{x \to 3^{-} } 9-3x= \lim_{x \to 3^{-} } 9-3*3=0

The right-hand limit

\lim_{x \to 3^{+} } x^{2} -x= \lim_{x \to 3^{+} } 3^{2}-3 =6

Because the limits are not the same the limit does not exist.

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Hernando ate StartFraction 2 Over 8 EndFraction of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told th
ozzi

Answer:

Yes, they are correct. Hernando divided 6 by 6.

Step-by-step explanation:

Given that:

Hernando ate 2/8 of a pizza for dinner.

Let the pizza be x. Then:

Hernando ate \dfrac{2}{8} \ \ o f  \ \ x

Then he gave the rest of the pizza to his friends

Hernando now carried out the  following calculations to support his activities;

\dfrac{6}{8} \div 6= \dfrac{6 \div 6}{8}= \dfrac{1}{8}

\dfrac{6}{8} \times \dfrac{1}{6}= \dfrac{6 \div 6}{8}= \dfrac{1}{8}

From the above calculation; we will see that Hernando divided 6 by 6 in both cases to get \dfrac{1}{8}.

Thus, the correct answer is:

Yes, they are correct. Hernando divided 6 by 6.

3 0
2 years ago
Read 2 more answers
Solve the following logarithmic equations.<br> log[(x^2 + 2x − 3)^4] = 0
saw5 [17]

Answer:

The solutions are x = 1.24 and x = -3.24

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log[(x² + 2x -3)⁴] = 0

Apply the logarithm property: log(xᵃ) = a log(x)

4 log[(x² + 2x -3)⁴] = 0

Divide by 4 both sides

log(x² + 2x -3) = 0

if log(x² + 2x -3) = 0, then  x² + 2x -3 = 1 because only log 1 = 0

x² + 2x -3 = 1

Subtract 1 at both sides of the equation

x² + 2x -4 = 0

Using the quadratic formula let´s solve this quadratic equation:

a = 1

b = 2

c = -4

x = [-b± √(b² - 4ac)]/2a

x =  [-2 + √(4 - 4(-4)·1)]/2 = 1.24

and

x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24

The solutions are x = 1.24 and x = -3.24

Have a nice day!

4 0
3 years ago
Justin earns a base salary of $1500 per month at
photoshop1234 [79]

Answer: $1500 + 3% + $82,975= 84475.03

Step-by-step explanation:

5 0
2 years ago
The regular price of an item is $65. The item is on sale with a discount of $8.What is the discount rate
amid [387]
The discount rate is the discount amount ($8) divided by the regular price, as a percentage.65/8=8.125 rounded to 8 so 8%.
6 0
2 years ago
Enter the explicit rule for the geometric sequence.
Sveta_85 [38]

Answer:  \frac{3}{2}(\frac{1}{2})^{n-1}

<u>Step-by-step explanation:</u>

\frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, ...

common ratio (r) = \frac{1}{2}

first term (a₁) = \frac{3}{2}

a_{n} = a₁ (r)ⁿ⁻¹

   = \frac{3}{2}(\frac{1}{2})^{n-1}

4 0
3 years ago
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