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3 years ago

If c(x)=5/x-2 and d(x)=x+3, what is the domain of (cd)(x)

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

6 0

I hope this helps you

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Lim x->pi/3 ((2cosx-1)/(tan^2x-3))

beks73 [17]

You can check that the limit comes in an undefined form:

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\dfrac{0}{0}$

In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:

$\dfrac{\text{d}}{\text{d}x}2\cos(x)-1 = -2\sin(x)$

and

$\dfrac{\text{d}}{\text{d}x}\tan^2(x)-3 = 2\dfrac{\tan(x)}{\cos^2(x)}=\dfrac{2\sin(x)}{\cos^3(x)}$

So, we have

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\lim_{x\to\frac{\pi}{3}} \dfrac{-2\sin(x)}{\frac{2\sin(x)}{\cos^3(x)}}=\lim_{x\to\frac{\pi}{3}}-\cos^3(x)=-\cos^3\left(\dfrac{\pi}{3}\right)$

6 0

3 years ago

Paige had $20 to spend on 6 pieces of candy. After buying the candy, she has $6.50 left. How much was each piece of candy?

irga5000 [103]

Answer:

$2.25

Step-by-step explanation:

1. 20-6.50= 13.50

2. 13.50/6(pieces of candy) = $2.25

8 0

3 years ago

Buses to exeter leave a bus station every 20 minutes.Buses to Plymouth leave the bus station every 16 minutes A bus to exeter an

Eva8 [605]

9:20 am
Lcm is 80 so 80 minutes after 8 am is 9:20

6 0

3 years ago

My ones digit is twice the hundreds digit

BlackZzzverrR [31]

The hundreds digit is twice as large as the ones digit. 3 doubled is 6, 6 doubled is 12, and 9 doubled is 18. Since 6 is the only option that is one digit, the hundreds digit must be 6 and the ones digit must be 3. The tens digit is five less than the hundreds digit.

3 0

3 years ago

Sally works as an estimator for G&J Electric. She has determined that 550 feet of electrical cable will be needed to wire a

GuDViN [60]

Given :

Initial length of electric cable needed, $L=550\ ft$ .

Later, Sally is told that the homeowner has decide to cut back from a three-car garage to a two-car garage, which will eliminate two branch circuits, one of 23 feet and the other of 34 feet.

To Find :

How many feet of wire will be needed now.

Solution :

Wire needed is given by :

Required = Total wire - ( length of 1nd branch + length of 2nd branch )

Required = 550 - ( 23 + 34 )

Required = 550 - ( 57 ) ft

Required = 443 ft

Therefore, length of wire required is 443 ft.

Hence, this is the required solution.

7 0

3 years ago