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makvit [3.9K]
1 year ago
5

exercise 5.2.6. let g be defined on an interval a, and let c ∈ a. (a) explain why g′(c) in definition 5.2.1 could have been give

n by g′(c)
Mathematics
1 answer:
Dahasolnce [82]1 year ago
3 0

From definition 5.2.1:

g'(c) = limₓ→c  g(x) ₋ g(c)/x₋c

Let h = x ₋ c

Then x = c₊h

substituting in the above defination we have:

g'(c) = limc₊h→c  g(c₊h) ₋ g(c)/c₊h₋c

=  limc₊h→c g(c₊h) ₋ g(c)/h

x → c ⇒ x ₋ c → 0 ⇒ h → 0

Hence we have,

limc₊h→c  g(c₊h) ₋ g(c)/h

Therefore we have defined clearly why g′(c) in definition 5.2.1 could have been given by g′(c).

Learn more about limits and continuity here:

brainly.com/question/24637240

#SPJ4

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Write and solve a proportion to answer the question. 36 is 0.9% of what number w? =0.9100
pickupchik [31]

Answer:

Step-by-step explanation:

The question can be written out like this:

36 = 0.009x

Multiply both sides by 1,000:

9x = 36,000

Divide both sides by 9:

x = 4,000

8 0
3 years ago
Please help figure out I will give brainliest!
noname [10]

Answer:

40 student 110 adult

this is using desmos

but to smash the equation you can go like basically we have to cancel out each variable to solve for the other

3x + 8y = 1000

x + y < =150

-3(x + y <= 150)

-3x -3y = -450

3x + 8y = 1000

5y = 550

y= 110

3x + 8 y = 1000

-8(x+y<=150) = -8x - 8y <= -1200

-5x = -200

\frac{ - 5x}{ - 5 }   = x

\frac{ - 200}{ - 5}  = 40

x= 40

40 kids 110 adults

7 0
2 years ago
You are given a line that has a slope of 4 and passed through the point (3/8, 1/2). Which statements about the question of the l
alexgriva [62]

Answer:

Statement 1, 2 and 4 are true where as statement 3 is not true.

Step-by-step explanation:

<u>Statement 1: The y-intercept is -1</u>

<em>Point (3/8, 1/2)</em>

<em>Slope = m = 4</em>

<em>y = mx + c</em>

<em>1/2 = 4(3/8) + c</em>

<em>1/2 = 3/2 + c</em>

<em>1/2 = 3/2 + 2c/2</em>

<em>-2 = 2c</em>

<em>c = -1 </em>

This statement is true as the y-intercept is -1.

<u>Statement 2: The slope intercept equation is y= 4x - 1</u>

<em>slope = m = 4</em>

<em>y-intercept = c = -1</em>

<em>y = mx + c</em>

<em>y = 4x - 1</em>

This statement is true as the slope intercept equation is y= 4x -1

<u>Statement 3: The point slope equation is y - 3/8 = 4 (x - 1/2)</u>

<em>Point slope equation: y - y1 = m (x - x1)</em>

<em>Points: (x, y) (3/8, 1/2)</em>

<em>y1 = 1/2</em>

<em>x1 = 3/8</em>

<em>Slope = m = 4</em>

<em>y - 1/2 = 4 (x - 3/8)</em>

This statement is not true as the slope intercept equation is y - 1/2 = 4 (x - 3/8) instead of y - 3/8 = 4 (x - 1/2).

<u>Statement 4: The point (3/8, 1/2) corresponds to (x1, y1) in the point slope form of the equation</u>

This statement is true as shown in statement 3's explanation where x1 = 3/8 and y1 = 1/2

!!

6 0
3 years ago
Which graph represents the solution set to the system of inequalities?
marta [7]
It should be the top left because the shaded area is below (or less than) the line -3/4x +1 and greater than the other line
8 0
2 years ago
Read 2 more answers
At a shelter,15% of the dogs are puppies. There ate 60 dogs at the shelter. How many are puppies?
Anna71 [15]
15% of 60

.15 × 60 = 9
5 0
2 years ago
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