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elena-14-01-66 [18.8K]
3 years ago
14

Please Help Quickly!!! Find the limit if f(x) = x^3

Mathematics
1 answer:
jeka943 years ago
4 0

Answer:

Option b. 12

Step-by-step explanation:

This exercise asks us to find the derivative of a function using the definition of a derivative.

Our function is f(x) = x^{3}. Therefore:

f(2+h) = (2+h)^{3}

f(2) = (2)^{3} = 8

Then:

\lim_{h \to \0} \frac{f(2+h)-f(2)}{h}=\lim_{h \to \0} \frac{(2+h)^{3}-8}{h}

Expanding:

\lim_{h \to \0} \frac{(2+h)^{3}-8}{h} =\lim_{h \to \0} \frac{8+ h^{3} +6h(2+h) -8}{h} =\lim_{h \to \0} \frac{h^{3} +6h(2+h)}{h}

\lim_{h \to \0} \frac{h^{3}+ 6h(2+h)}{h} =\lim_{h \to \0} h^{2} + 6(2+h)

Now, if x=0:

\lim_{h \to \0} \frac{f(2+h)-f(2)}{h} = (0)^{2} +6(2+0) = 12

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Equation parallel to y = 3x + 2 and passing through (1, 1)
Kisachek [45]

Answer:

y = 3x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, then

y = 3x + c ← is the partial equation

To find c substitute (1, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = 3x - 2 ← equation of line

6 0
3 years ago
People attending a football game either supported the home team or the visiting team. if 1369 of the people attending supported
Masja [62]

Given the number of the people attending the football game, the percentage supporters for the home team is 37%.

<h3>What is Percentage?</h3>

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given the data in the question;

  • Number of home team supporters nH = 1369
  • Number of visting team supporters nV = 2331
  • Percentage of supporters for home team PH = ?

For we determine the total number of people attending the football game;

nT = nH + nV

nT = 1369 + 2331

nT = 3700

Now, using the perecentage formula above, we find the Percentage of supporters for home team PH

Percentage = ( Part / Whole ) × 100%

PH = ( nH/ nT) × 100%

PH = ( 1369/ 3700) × 100%

PH = 0.37 × 100%

PH = 37%

Therefore, given the number of the people attending the football game, the percentage supporters for the home team is 37%.

Learn more about Percentages here: brainly.com/question/24159063

#SPJ1

6 0
2 years ago
What is 2 + 2. Express answer as a fraction
jekas [21]
2+2 = 4 therefore four as a fraction would just be four wholes —-> 4/1
3 0
2 years ago
Read 2 more answers
7-ounce package costs $2.59. A 12 ounce package costs $4.56. An 18 ounce package costs $6.30. Which package is the best buy?
Yanka [14]

Answer:

18 ounce package for $6.30

Step-by-step explanation:

For each one, you divide the money by the package to see how much it is per ounce.

2.59 / 7 = $0.37 per oz

4.56 / 12 = $0.38 per oz

6.30 / 18 = $0.35 per oz

4 0
3 years ago
On a coordinate grid, Ming's house is located 2 blocks to the right and blocks up from (0. 0). Joe's house is located 3 blocks t
kolbaska11 [484]
If o<span>n a coordinate grid, Ming's house is located 2 blocks to the right and (I suppose also 2) blocks up from (0. 0), then the ordered pair that describes the location of Ming's house is (2,2) (moving right 2 units from some point you have to add 2 units to the x-coordinate of the point from which you are moving and moving up 2 units from this point you have to add 2 units to y-coordinate of the point from which you are moving up).
</span>
If Joe's house is located 3 blocks to the right and 2 blocks down from Ming's house, then the ordered pair that describes the location of Ming's house is (2+3,2-2), that is (5,0) <span><span>(moving right 3 units from some point you have to add 3 units to the x-coordinate of the point from which you are moving and moving down 2 units from the point you have to substract 2 units from y-coordinate of the point from which you are moving down)</span>.</span>


3 0
3 years ago
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