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4 years ago

Find limit as x approaches -3- of x/(sqrt(x^2-9)

Mathematics

1 answer:

gregori [183]4 years ago

5 0

$lim_{x \rightarrow -3} \frac{x}{x^2-9} =lim_{x \rightarrow -3} \frac{1}{2x} = \frac{1}{2(-3)} =- \frac{1}{6}$

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Solve. -317 - 221 - (-354) A. 892 B. -892 C. 184 D. -184

Liula [17]

−317−221−(−354)=
−538−(−354)=
−184

so it would be d

8 0

3 years ago

Help with 5b please . thank you.

Allushta [10]

Answer:

See explanation

Step-by-step explanation:

We are given f(x)=ln(1+x)-x+(1/2)x^2.

We are first ask to differentiate this.

We will need chain rule for first term and power rule for all three terms.

f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x

f'(x)=(0+1)/(1+x)-(1)+x

f'(x)=1/(1+x)-(1)+x

We are then ask to prove if x is positive then f is positive.

I'm thinking they want us to use the derivative part in our answer.

Let's look at the critical numbers.

f' is undefined at x=-1 and it also makes f undefined.

Let's see if we can find when expression is 0.

1/(1+x)-(1)+x=0

Find common denominator:

1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0

(1-1-x+x+x^2)/(1+x)=0

A fraction can only be zero when it's numerator is.

Simplify numerator equal 0:

x^2=0

This happens at x=0.

This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.

So we should see increasing values of f when we up the value for x after 0.

Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.

So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.

8 0

3 years ago

Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 Determine the quartiles.

worty [1.4K]

Answer:

Lower quartile= 4.75

Middle quartile= 9.5

Upper quartile= 14.25

Step-by-step explanation:

The given date set is 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

On counting them we notice that it's number of element is 18

So N = 18

Arranging them in ascending order gives

12,18,18,20,23,24,24,25,25,29,31,43,43,43,53,53,65,78

Lower quartile= (N+1)*1/4

Lower quartile= (18+1)/4

Lower quartile= 19/4

Lower quartile= 4.75

Middle quartile= (N+1)*2/4

Middle quartile= (18+1)*2/4

Middle quartile= (19)*2/4

Middle quartile= 9.5

Upper quartile= (N+1)*3/4

Upper quartile= (18+1)*3/4

Upper quartile= (19)*3/4

Upper quartile= 14.25

Inter quartile range = upper quartile- minutes lower quartile

= 14.25-4.75

= 9.5

4 0

3 years ago

WHERES THE BEEF??????????????????? hehehe sorry ab that im just HELLA bored over here ;)

ddd [48]

Me too tbhh school sucks omggg I have to put like an equation because If

5 0

3 years ago

Find the slope of the line passing through the points A(0, 7) and B(- 3, 0)

klasskru [66]

Answer:

not sure. though good luck and have a good day :)

Step-by-step explanation:

6 0

4 years ago