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Fudgin [204]
3 years ago
8

Use the definition of continuity and the properties of limits to show that the function

Mathematics
1 answer:
Zepler [3.9K]3 years ago
7 0

Answer:

Applied the definition and the limit.

They had the same result, so the function is continuous.

Step-by-step explanation:

At function f(x) is continuous at x = a if:

\lim_{x \to a} f(x) = f(a)

In this question:

f(x) = x^{2} + 5(x-2)^{7}

At x = 3.

\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14

f(3) = 3^{2} + 5(3-2)^{7} = 14

Since \lim_{x \to 3} f(x) = f(3), f(x) is continuous at x = 3.

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8х + 5у = -7<br> — 7х + бу = — 4
Levart [38]

Answer: x = -0.2651 and y = -0.9759

Step-by-step explanation:

Solution by substitution method

8x+5y= -7

-7x+6y= -4 = 7x-6y=4

Suppose,

8x+5y=-7→(1)

7x-6y=4→(2)

Taking equation (1), we have

8x+5y= -7

⇒8x= -5y -7

⇒x= -5y-7 / 8 →(3)

Putting x= -5y-7 / 8

in equation (2), we get 7x-6y=4

7(-5y-7/8)-6y=4

⇒-35y-49-48y=32

⇒-83y-49=32

⇒-83y=32+49

⇒-83y=81

⇒y= 81 / -83

⇒y= -0.9759→(4)

Now, Putting y= -0.9759 in equation (3), we get

x= -5y-7

x= -5(-0.9759)-7/8

⇒x= 4.8795-7/8

⇒x= -2.1205/8

⇒x= -0.2651

∴x= -0.2651 and y = -0.9759

7 0
3 years ago
Convert 150 meters per second into miles per day
statuscvo [17]
 just divide it is simple bruh
3 0
3 years ago
write the equation of the line, with the given properties, in slope-intercept form. slope = -5, through (-4,4)
Daniel [21]

Answer: y=-5x-16

Step-by-step explanation:

Since we are given the slope and the point, we can plug in the point to solve for y-intercept.

4=-5(-4)+b          [multiply]

4=20+b               [subtract both sides by 20]

b=-16

Now, we know the equation is y=-5x-16.

3 0
3 years ago
Find the perimeter of the semicircle when diameter is 3.5 cm. (1 Point)
Feliz [49]

● Answer:

8.995 cm

● Step-by-step explanation:

P = d + L/2

d = 3.5 cm

L/2 = 2pi×r/2

= pi×d/2

= 3.14×3.5/2

= 5.495 cm

P = 3.5cm + 5.495

= 8.995 cm

8 0
4 years ago
Consuela earns a salary of 40000$ per year plus commission of 1000$ for each car she sells. Write and solve an equation that sho
iVinArrow [24]
40000+1000x=60000
-40000. -40000

1000x=20000
x=20
6 0
3 years ago
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