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2 years ago

Find the derivative of f(x)=x+1/x-1 using first principal

Mathematics

1 answer:

zepelin [54]2 years ago

5 0

f ' ( x ) = 1 ( x + 1 ) 2

Explanation:

differentiating from first principles

f ' ( x ) = lim h → 0

f ( x + h ) − f ( x ) h

f ' ( x ) = lim h → 0

x + h x + h + 1 − x x + 1 h

the aim now is to eliminate h from the denominator

f ' ( x ) = lim h =0

( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )

f ' ( x ) = lim h → 0

x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )

f ' ( x ) = lim h → 0

h 1 h 1 ( x + 1 ) ( x + h +1 )

f ' ( x ) = 1 ( x + 1 ) 2

You might be interested in

3) Divide x3 + 4x2 – 3x – 12 by (x + 4)

alex41 [277]

Answer:

Factor the numerator and denominator and cancel out the common factors.

x ^2 − 3 is your final answer.

Step-by-step explanation:

Hope that this helps you out! :)

If you have any questions please put them in the comment section below this answer.

Have a great rest of your day/night!

Please thank me on my profile if this answer has helped you.

7 0

2 years ago

What is 2x =6.5 And how

Leona [35]

Answer:

Step-by-step explanation:

2x =6.5

To find the value of x, divide both sides by 2 so you will have 1x.

x = 3.25

8 0

1 year ago

Read 2 more answers

I need help understanding this and help with the problems...

Pavel [41]

1. 15+37=?

15=10+5 (given on the diagram)
37=30+7 (given on the diagram)
add digits to digits 5+7=12=10+2
add tens to tens 10+30+10=50
add tens and digits 50+2=52.

2. 22+49=?

22=20+2 (given on the diagram)
49=40+9 (given on the diagram)
add digits to digits 2+9=11=10+1
add tens to tens 20+40+10=70
add tens and digits 70+1=71.

3. 38+26=?

38=30+8 (given on the diagram)
26=20+6 (given on the diagram)
add digits to digits 8+6=14=10+4
add tens to tens 30+20+10=60
add tens and digits 60+4=64.

Answer: 1) 52; 2) 71; 3) 64.

7 0

2 years ago

Read 2 more answers

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately

Genrish500 [490]

Answer:

a) 0.057

b) 0.5234

c) 0.4766

Step-by-step explanation:

To find the p-value if the sample average is 185, we first compute the z-score associated to this value, we use the formula

$z=\frac{\bar x-\mu}{\sigma/\sqrt N}$

where

$\bar x=mean\; of\;the \;sample$

$\mu=mean\; established\; in\; H_0$

$\sigma=standard \; deviation$

N = size of the sample.

So,

$z=\frac{185-175}{20/\sqrt {10}}=1.5811$

$\boxed {z=1.5811}$

As the sample suggests that the real mean could be greater than the established in the null hypothesis, then we are interested in the area under the normal curve to the right of 1.5811 and this would be your p-value.

We compute the area of the normal curve for values to the right of 1.5811 either with a table or with a computer and find that this area is equal to 0.0569 = 0.057 rounded to 3 decimals.

So the p-value is

$\boxed {p=0.057}$

Since the z-score associated to an α value of 0.05 is 1.64 and the z-score of the alternative hypothesis is 1.5811 which is less than 1.64 (z critical), we cannot reject the null, so we are making a Type II error since 175 is not the true mean.

We can compute the probability of such an error following the next steps:

Step 1

Compute $\bar x_{critical}$