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BaLLatris [955]
3 years ago
15

Limits of a Function

Mathematics
2 answers:
Novay_Z [31]3 years ago
8 0

<u>We are given the equation:</u>

<u></u>\lim_{x \to 1} \frac{f(x)-8}{x-1} = 10<u></u>

which can be rewritten as:

<u></u>\frac{\lim_{x \to 1}[f(x)-8]}{\lim_{x \to 1}[x-1]} = 10<u></u>

<u></u>\lim_{x \to 1}[f(x)-8] = 10*\lim_{x \to 1}[x-1]<u></u>

<u></u>\lim_{x \to 1}[f(x)-8] = \lim_{x \to 1}[10x-10]<u></u>

which means that..

f(x) - 8 = 10x - 10

f(x) = 10x - 10 + 8

f(x) = 10x - 2

<u>Finding the limit:</u>

<u />\lim_{x \to 1} f(x) =  \lim_{x \to 1} (10x - 2)<u />

<u />\lim_{x \to 1} f(x) =  10(1) - 2<u />

<u />\lim_{x \to 1} f(x) =  8<u />

ICE Princess25 [194]3 years ago
8 0

Answer:

8.

Step-by-step explanation:

Limit x --> 1  of (10x - 2 - 8) / (x - 1)   ( BY L'HOPITALS RULE)

=   10/1 = 10.

so f(x) = 10x - 2

The limit as this as x ---> 1 is 8.

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5 0
3 years ago
Can i have the answer to this <br> pic is below
eduard

Answer:

question 1: m = 3/2

question 2: m = 1/95

Step-by-step explanation:

Slope intercept form of equation is of form

y = mx+c

where m is the slope of line and c is the y intercept of the line.

Y intercept is point on y axis where the line intersects the y axis.

____________________________________

given

y = 3/2 x

comparing it with y = mx+c

we have m = 3/2 .

since y = 3/2 x does not have constant term so it can be taken as 0. hence c is 0

_________________________________________

slope for any two point (x1,y1) and (x2,y2) on coordinate plane is given by

slope = (x2-x1)/y2-y1)

From the given table lets take two point as (2,190) and(4,380)

Thus, slope m is given by

m = (4-2)/(380-190) = 2/190 = 1/95

m = 1/95

Though, slope can be taken by dividing y by x (y/x). It is good practice to use two point form formula as given above . Provided two points are given

Please mark it the brainliest.

4 0
3 years ago
Solve for x leave answer as decimal <br> 6/5=x/3
777dan777 [17]

Answer:

3 3/5 =x

3 .6 =x

Step-by-step explanation:

6/5 = x/3

Use cross products

6*3 = 5*x

18 = 5x

Divide each side by 5

18/5 = 5x/5

18/5 =x

3 3/5 =x

8 0
3 years ago
Read 2 more answers
What are the restrictions on the domain of g o h?
umka21 [38]

g(x) = \sqrt{x-4} and h(x)= 2x-8

g o h is a composition function

First we find g o h

g o h is g(h(x))

We plug in h(x) in g(x)

We replace x  with 2x-8 in g(x)

g(h(x)) = g (2x-8) = \sqrt{2x-8-4} = \sqrt{2x-12}

g(h(x)) = \sqrt{2x-12}

To find domain we look at the domain of h(x) first

Domain of h(x) is set of all real numbers

now we look at the domain of g(h(x))

Negative number inside the square root is imaginary. so we ignore negative number inside the square root

So to find domain we set 2x - 12 >=0   and solve for x

2x - 12 >=0

add both sides by 12

2x >= 12

divide both sides by 2

x > = 6



5 0
3 years ago
Read 2 more answers
I WILL GIVE BRAINLIEST IF U CAN HELP ME WITH ANY OF MY QUESTIONS!!!
faltersainse [42]

Answer:

12.5

Step-by-step explanation:

square root of 10^2 - 8^2 = 6 gives us missing side

sin^-1(8/10) = 53.13 gives us half of the angle

90-53.13 = 36.869 gives us the angle of the triangle on the right

tan(36.869) x 6 = 4.5

4.5 + 8 = 12.5

Hope that helps,

Good Luck! x

3 0
3 years ago
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