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Virty [35]
2 years ago
9

Lim t^4 - 6 / 2t^2 - 3t + 7

Mathematics
1 answer:
Harman [31]2 years ago
6 0

I think you meant to say

\displaystyle \lim_{t\to2}\frac{t^4-6}{2t^2-3t+7}

(as opposed to <em>x</em> approaching 2)

Since both the numerator and denominator are continuous at <em>t</em> = 2, the limit of the ratio is equal to a ratio of limits. In other words, the limit operator distributes over the quotient:

\displaystyle \lim_{t\to2} \frac{t^4 - 6}{2t^2 - 3t + 7} = \frac{\displaystyle \lim_{t\to2}(t^4-6)}{\displaystyle \lim_{t\to2}(2t^2-3t+7)}

Because these expressions are continuous at <em>t</em> = 2, we can compute the limits by evaluating the limands directly at 2:

\displaystyle \lim_{t\to2} \frac{t^4 - 6}{2t^2 - 3t + 7} = \frac{\displaystyle \lim_{t\to2}(t^4-6)}{\displaystyle \lim_{t\to2}(2t^2-3t+7)} = \frac{2^4-6}{2\cdot2^2-3\cdot2+7} = \boxed{\frac{10}9}

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Cual es la utilidad de la representacion a escala de diferentes distancias reales
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Answer:

Scales are used to represent real distances and proportions into maps and planes, that way we can have a bigger perspective about something just having in paper.

One direct use of scales are seen in architecture plans, there, the architect uses scales to represent the construction he is designing. Also, the architect can have a more complete point of view about the principial elements on his work.

6 0
2 years ago
Given: ABCD is a parellelogram.<br><br> Prove: AB=CD and BC=DA
ozzi

Answer:


Step-by-step explanation:

We have given a parallelogram ABCD.

For a parallelogram,

Opposite pair of sides are parallel to each other.

i.e AD is parallel to BC and AB is parallel to CD.

From the attached figure,

∡1 = ∡4  and  ∡2 = ∡3    {If two parallel lines cut by a transversal line then alternate interior angles are congruent }

Next, AC ≅ AC  {Reflexive identity}

hence, ΔABC ≅ ΔCDA   , By Angle-Side-Angle(ASA) congruent property of triangle.

Therefore, AB = CD  and AD = BC   {Proved}


6 0
2 years ago
Read 2 more answers
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4 0
2 years ago
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d
kozerog [31]

Answer: 49.85%

Step-by-step explanation:

Given : The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e.  \mu=61 and \sigma=9

To find :  The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and 34+3(9).

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between \mu and \mu+3(\sigma). (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between \mu and \mu+3(\sigma) = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%

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2 years ago
Write expressions for 4 consecuative integers.
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