All categories

3 years ago

Use the definition of a derivative to find f’(x).

Mathematics

1 answer:

tatyana61 [14]3 years ago

7 0

Answer:

f'(x) = $-\frac{9}{x^2}$

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x) = $$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}$

$= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$$

You might be interested in

Question 9 of 10 Which of the following statements must be true about this diagram? Check all that apply. 10 A. x+y=w B. W> Y

Nataliya [291]

Answer:

<h2>MY ANSWER IS E.</h2>

HOPE IT HELPS ❤️

8 0

2 years ago

A decimal is a fraction that has a denominator of 100. A. Sometimes B. always C. Never

kolezko [41]

Always is the answer. becuz .2 is 20/100. i like math so ik

6 0

3 years ago

Read 2 more answers

A diesel train traveled to the repair yards and

jek_recluse [69]

Answer:

B. 16 hrs

Step-by-step explanation:

Distance = rate × time

The best way to do this is to make a table with the info. We are concerned with the trip There and the Return trip. Set it up accordingly:

d = r × t

There

Return

The train made a trip from A to B and then back to A again, so the distances are both the same. We don't know what the distance is, but it doesn't matter. Just go with it for now. It'll be important later.

d = r × t

There d

Return d

We are also told the rates. There is 70 km/hr and return is 80 km/hr

d = r × t

There d = 70

Return d = 80

All that's left is the time column now. We don't know how long it took to get there or back, but if it took 2 hours longer to get There than on the Return, the Return trip took t and the There trip took t + 2:

d = r × t

There d = 70 × t+2

Return d = 80 × t

The distances, remember, are the same for both trips, so that means that by the transitive property of equality, their equations can be set equal to each other:

70(t + 2) = 80t

70t + 140 = 80t

140 = 10t

14 = t

That t represents the Return trip's time. Add 2 hours to it since the There trip's time is t+2. So 14 + 2 = 16.

B. 16 hours

8 0

3 years ago

Use una variable para escribir una expresión para representar: catorce más que el cociente de ciento doce y algún número a. 14 &

jeyben [28]

Answer:

b. 14 + (112 ÷ n)

Step-by-step explanation:

En esta pregunta la opcion que deberiamos elegir seria 14 + (112 ÷ n). En esta expresion primero se divide 112 por algun numero que es representado por el variable n. Luego de obtener el cociente de esta division, se le agrega 14 al cociente. Esto nos daria un valor nuevo y representa perfectamente la frase en esta pregunta... catorce más que el cociente de ciento doce y algún número

8 0

3 years ago

An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume

Elis [28]

Answer:

The final pressure of the gas when its temperature returns to its initial value $1.8234\times 10^6$ Pa.

Step-by-step explanation:

Given : An ideal gas is confined within a closed cylinder at a pressure of $2.026\times 10^5$ Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.