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GrogVix [38]
3 years ago
13

Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024

h
Mathematics
1 answer:
kupik [55]3 years ago
4 0
\displaystyle\lim_{h\to0}\frac{(4+h)^5-1024}h=\lim_{h\to0}\frac{(4+h)^5-4^5}h

Recall the definition of the derivative of a function f(x) at a point x=c:

f'(c)=\displaystyle\lim_{h\to 0}\frac{f(c+h)-f(c)}h

We can then see that f(c)=c^5, and by the power rule we have f'(c)=5c^4. Then replacing c=4, we arrive at

\displaystyle\lim_{h\to0}\frac{(4+h)^5-4^5}h=5\times4^4=1280

Alternatively, we could have expanded the binomial, giving

\dfrac{(4+h)^5-4^5}h=\dfrac{(4^5+5\times4^4h+10\times4^3h^2+10\times4^2h^3+5\times4h^4+h^5)-4^5}h
=\dfrac{1280h+640h^2+160h^3+20h^4+h^5}h
=1280+640h+160h^2+20h^3+h^4

and so as h\to0 we're left with 1280, as expected.
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Help please
ddd [48]

Answer:

  • B. When the peak temperature is 40°C, 72 units of electricity are used on average.

Step-by-step explanation:

We see the relationship is closer to linear in the interval 30 to 40

<u>Approximate points:</u>

  • (30, 34) and (34, 54)

<u>The slope of the line:</u>

  • m = (54 - 34)/(34- 30) = 20/4 = 5

<u>The line is:</u>

  • y - 34 = 5(x - 30)
  • y = 5x - 116

<u>At x = 40, the value of y would be:</u>

  • y = 5*40 - 116 = 84

The closet option is B

7 0
3 years ago
8. Starting from 300 feet away, a car drives toward you. It then passes by you at a speed of 48 feet per
fgiga [73]

Answer:

About 2 seconds away from you

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What is the equation of a line that passes through point R(3,7) and has a slope of 6?
djyliett [7]
The answer in slope intercept form is y = 6x-11

If you want the answer in standard form, then it would be 6x-y =11

notes:
* Slope intercept form is y = mx+b
* Standard form is Ax+By = C
=====================================

Explanation:

The given slope is m = 6
The line goes through (x,y) = (3,7)

Plug those three values into the equation below. Isolate b
y = mx+b
7 = 6*3+b
7 = 18+b
7-18 = 18+b-18 ... subtract 18 from both sides
-11 = b
b = -11

So because m = 6 and b = -11, this means y = mx+b turns into y = 6x-11

The answer in slope intercept form is y = 6x-11

To convert to standard form Ax+By = C, we just have to get all the x and y terms together on the same side. I'm going to move the y term to the right side and move the 11 to the left side

y = 6x-11
y+11 = 6x-11+11
y+11 = 6x
y+11-y = 6x-y
11 = 6x-y
6x-y = 11

The answer in standard form is 
6x-y = 11
which is a different way to write the same line

4 0
3 years ago
It me again I need help
9966 [12]

Answer:

85%

Step-by-step explanation:

He  hit it 17/20

We want that as a percent

Multiply by 5/5

17/20*5/5 = 85/100

Percent means out of 100

85%

3 0
3 years ago
Read 2 more answers
Consider Frank's math test scores for the semester. Find the interquartile range of the scores.
musickatia [10]
Okay so you put the numbers in order:
70, 74, 81, 82, 83, 91, 94.

Then you find the median which will be Q2:
82.

Once you have the total median, you find the midpoint of the first and last part:
70, 74, 81. Midpoint/Q1=74
83, 91, 94. Midpoint/Q3=91

Now that you have that, you subtract Q3 and Q1.
91-74=17

17 is your IQR.
4 0
3 years ago
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