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nikitadnepr [17]
3 years ago
6

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity]

ln(5x) 5x Step 1 As x → [infinity], ln(5x) → and 5x → .
Mathematics
1 answer:
Kobotan [32]3 years ago
6 0

Answer:

\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0

Step-by-step explanation:

L'Hopital's rule says that, if both numerator and denominator diverge, then we can look at the limit of the derivates.

Here we have:

\lim_{x \to \infty} \frac{ln(5x)}{5x}

The numerator is ln(5x) and when x tends to infinity, this goes to infinity

the denominator is 5x, and when x tends to infinity, this goes to inifinity

So both numerator and denominator diverge to infinity when x tends to infinity.

Then we can use L'Hopithal's rule.

The numerator is:

f(x) = Ln(5x)

then:

f'(x) = df(x)/dx = 1/x

and the denominator is:

g(x) = 5*x

then:

g'(x) = 5

So, if we use L'Hopithal's rule we get:

\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0

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Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Mon
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Answer:

Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2

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3 years ago
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A triangle has sides with lengths of 60 feet, 63 feet, and 87 feet. Is it a right triangle?
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Answer:

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Step-by-step explanation:

We can use the Pythagorean Theorem to check if this triangle is a right triangle:

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Substitute the lengths of the sides into the equation:

60^2+63^2=87^2

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state domain and range, intercepts, relative max and relative mins points and values, intervals of increase and decrease, interv
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The domain of the graph is -∝ < x < ∝ and the range of the graph is -∝ < y < ∝. Also, the graph has no axis of symmetry

<h3>The domain and range of the graph</h3>

From the graph, we can see that the x values extend indefinitely

So, the domain of the graph is -∝ < x < ∝

From the graph, we can see that the y values extend indefinitely

So, the range of the graph is -∝ < y < ∝

<h3>The intercepts</h3>

This is where the graph crosses the axes

So, we have the intercepts to be

  • x-intercept = -4, -2 and 2
  • y-intercept = -9

<h3>Relative max and relative mins points and values, </h3>

The graph has a relative maximum at (3, 3) and the relative minimum are (0.5, 10)

<h3>Intervals of increase and decrease, </h3>

There are the intervals where the function increases and decreases

So, we have the intervals to be

  • Increasing interval: (0.5, ∝) and (-∝, -3)
  • Decreasing interval: (-3, 0.5)

<h3>Intervals of positive and negative,</h3>

There are the intervals where the function is positive and negative

So, we have the intervals to be

  • Positive interval: (-4, -2) and (2, ∝)
  • Negative interval: (-∝, -4) and (-2, 2)

<h3>The symmetry</h3>

This is the line that divides the graph equal part

In this case, the graph has no axis of symmetry

<h3>The end behavior</h3>

Using the intervals where the function is positive and negative, the end behavior is

  • As x ⇒ ∝, f(x) ⇒ +∝
  • As x ⇒ -∝, f(x) ⇒ -∝

Read more about functions at:

brainly.com/question/3951754

#SPJ1

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