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Answer:

[tex] \displaystyle \: \frac{5}{4} [/tex]

Step-by-step explanation:

we are given a expression

we are said to solve it using L'Hôpital's Rule

recall, L'Hôpital's Rule:

[tex] \displaystyle \lim _{x \to \: c}( \frac{f(x)}{g(x)} ) = \lim _{x \to \: c} \frac{f ^{'}(x) }{ {g}^{'}(x) } [/tex]

it is to say the ' means derivative

our given expression:

[tex]\displaystyle\lim_{ x\to 2}\frac{x^2+x-6}{x^2-4}[/tex]

let's apply L'Hôpital's Rule

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2+x-6)}{ \dfrac{d}{dx} (x^2-4)}[/tex]

some formulas of derivative

[tex] \displaystyle \: \frac{d}{dx} {x}^{n} = {nx}^{n - 1} [/tex]

[tex] \displaystyle \: \frac{d}{dx} {x}^{} = 1[/tex]

[tex] \displaystyle \: \frac{d}{dx} {c}^{} = 0[/tex]

[tex] \sf \displaystyle \: \frac{d}{dx} {f}^{} (x) + {g}^{}(x) = {f}^{'} (x) + {g}^{'}(x)[/tex]

use sum derivative formula to simplify:

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2)+ \dfrac{d}{dx} (x) + \dfrac{d}{dx}( -6)}{ \dfrac{d}{dx} (x^2) + \dfrac{d}{dx} (-4)}[/tex]

simplify using exponents using exponent derivative formula:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ \dfrac{d}{dx} (x) + \dfrac{d}{dx}( -6)}{ 2x + \dfrac{d}{dx} (-4)}[/tex]

use variable derivative formula to simplify variable:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ 1+ \dfrac{d}{dx}( -6)}{ 2x + \dfrac{d}{dx} (-4)}[/tex]

use constant derivative formula to simplify derivative:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ 1+ 0}{ 2x + 0}[/tex]

simplify addition:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ 1}{ 2x }[/tex]

since we are approaching x to 2

we can substitute 2 for x

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2.2+ 1}{ 2.2 }[/tex]

simplify multiplication:

[tex]\displaystyle\frac{ 4+ 1}{ 4}[/tex]

simplify addition:

[tex] \displaystyle \: \frac{5}{4} [/tex]

hence,

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2+x-6)}{ \dfrac{d}{dx} (x^2-4)} = \frac{5}{4} [/tex]

Answer:

5/4 is your answer hope it helps

Answer:

-42

Step-by-step explanation:

8 + (-10)5 = 8-50 = -42

Answer:

No

Step-by-step explanation:

For this triangle to be a right triangle the following has to happen:

a^2 + b^2 = c^2

a=3, b=9, c= 12

3^2+9^2 does not equal 12^2

9+81 = 90        12^2 = 144

90 does not equal 144 so is not a right triangle

Answer:

see explanation

Step-by-step explanation:

Using converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = 12 , then 12² = 144

3² + 9² = 9 + 81 = 90 ≠ 144

Thus the triangle is not right.

Answer:

c. 66m

hope that helps!

Answer:

C. 66m

Step-by-step explanation:

Perimeter = 6 + 6 + 8 + 19 + 8 + 13 + 6 = 66m

Hope that helps!

ahoj odpoveď je 你好，答案是

Answer:

Mean- 5

median- 4

Mode- 2

Answer:

if the cubes represent 1 unit then:

y-intercept=

blue line: 1

red line: 4

green line: 7

slope=

blue line: 1/5

red line: 5/3

green line: 5/6

Step-by-step explanation:

i hope this helps :)

Answer:

Step-by-step explanation:

Answer: 20 months

explanation: You subtract 8 from 28 since 8 is the amount he had before he joined. He also said he planned on reading 1 book per month after joining the club. You want to subtract the 8 since it isn't relevant to the book club books read.

Answer:

Solution

Step-by-step explanation:

If im wrong let me know okay!

If im wrong Im sorry Im only 15 and im working here to help

Answer:

$15 + $2 = h

Step-by-step explanation:

( h = per hour) lilly rents a bike for $15 plus $2 per hour,

Answer:

independent

Step-by-step explanation:

f(x+3) means that when x is x + 3, what is y? X is always the input or the independent variable while y is dependant on y.

Answer:

c gsudhdbxjxjsjsbhxidhsv susb

Answer:

x=  10 −  129  i−1   ≈−0.1−1.135781669i

Step-by-step explanation:

(10x^2+3) - (-2x-10) = 10x^2+2x+13

Answer:

RL=5x+28 and

RO=8X-11

diagonal of square bisect equally the side

:.5x+28=8x-11

11+28=8x-5x

39=3x

x=39/3=13

RY=RL=5x+28=5×13+28=93If the answer is 93, move to answer.

Answer:

Dividing decimals +×÷=

Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Answer:

30

Step-by-step explanation:

took the test

Answer:

24

Step-by-step explanation:

6 x 4 = 24

Answer:

29, and 36

Step-by-step explanation:

65-7= 58

58/2= 29

29+7= 36

Answer:

29 and 36

Step-by-step explanation:

65 split in two since there are 2 people is 32.5

Since there is a 7 year difference, split 7 in half also which is 3.5

Subtract 3.5 from 32.5 to get the younger ones age and and add 3.5 to 32.5 to get the older one's age.

32.5-3.5= 29

32.5+3.5= 36

Answer:

Dependent variable: total distance (d)

Independent variable: number of hours (h)

Equation: d = 6h

Step-by-step explanation:

In this case given, the dependent variable, total distance (d), is dependent on the independent variable, number of hours (h). This is because, a change in the value of h leads to the change in the value of d. In order words, total distance (d) is a function of the number of hours (h).

Therefore:

Dependent variable: total distance (d)

Independent variable: number of hours (h)

Rate: 6 miles/hr

Equation: d = 6h

Answer:

57.5

Step-by-step explanation:

(180-65)/2

Answer:

X=reference angle, 8=opposite side, and 11 is the hypoteneuse

Answer:

total surface area = 79.8 cm^2

Step-by-step explanation: open up the prism into nets, and it has a base of 3 and height of 2.6. do 1/2 times 3 times 2.6=3.9*2=7.8.  Then do 3(3*8)=72. 72+7.8=79.8. I believe this is the answer to the best of my ability, hope this helps.

Answer:

1/4

Step-by-step explanation:

Use PhotoMath (:

Answer:

b) 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need to give all the fractions a common denominator so you can compare the numerators.

The least common multiple of 5, 8, 16, 4, 3 is 240.

⅖ = 96/240

⅞ = 210/240

15/16 = 225/240

¾ = 180/240

⅜ = 90/240

⅓ = 80/240

The only numerator between 96 and 210 is 180.

180/240 = ¾

⅖ < ¾ < ⅞

Answer

x = 18

You're welcome

Answer:

The answer would be x=18

Answer:

p+p+p = 1/2 or 3p=1/2

Step-by-step explanation:

Answer:

x = 72

Step-by-step explanation:

We set the two equal to each other

x = 12/y = 9 is equal to x/y = 54.

In order for 9 to get to 54, you have to multiply it by 6. Since you multiplied the denominator with 6, you have to do the same with the numerator. 12 times 6 is 72.

x = 72