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3 years ago

How do you do this ?

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

7 0

So the 3x means three times then u multiply by three

Arlecino [84]3 years ago

3 0

Fg is 9 because 3 times 3 is 9

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A) Use the limit definition of derivatives to find f’(x)

Ann [662]

$\text{Given that,}\\\\f(x) = \dfrac{ 1}{3x-2}\\\\\text{First principle of derivatives,}\\\\f'(x) = \lim \limits_{h \to 0} \dfrac{f(x+h) - f(x) }{ h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{1}{3(x+h) - 2} - \tfrac 1{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{1}{3x+3h -2} - \tfrac{1}{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{3x-2-3x-3h+2}{(3x+3h-2)(3x-2)}}{h}\\\\\\$

$~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{-3h}{(3x+3h-2)(3x-2)}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{-3h}{h(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \lim \limits_{h \to 0} \dfrac{1}{(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \cdot \dfrac{1}{(3x+0-2)(3x-2)}\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)(3x-2)}\\\\\\~~~~~~~=-\dfrac{3}{(3x-2)^2}$

$\text{Given that,}~\\\\f(x) = \dfrac{1}{3x-2}\\\\\textbf{Power rule:}\\\\\dfrac{d}{dx}(x^n) = nx^{n-1}\\\\\textbf{Chain rule:}\\\\\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}\\\\\text{Now,}\\\\f'(x) = \dfrac{d}{dx} f(x)\\\\\\~~~~~~~~=\dfrac{d}{dx} \left( \dfrac 1{3x-2} \right)\\\\\\~~~~~~~~=\dfrac{d}{dx} (3x-2)^{-1}\\\\\\~~~~~~~~=-(3x-2)^{-1-1} \cdot \dfrac{d}{dx}(3x-2)\\\\\\~~~~~~~~=-(3x-2)^{-2} \cdot 3\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)^2}$

8 0

2 years ago

Find the equation of the line shown

stiks02 [169]

Answer:

y = -2x+9

negative slope starts at 9 ( y intercept)

3 0

2 years ago

Emily predicted her car payment to be

miv72 [106K]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A pile of gravel is in the shape of a cone. The radius of the pile of gravel is 9 feet at the base. The height of the pile of gr

vitfil [10]

Answer:

678.24 cubic feet.

Step-by-step explanation:

A pile of gravel is in the shape of a cone.

Radius of base of cone (r) = 9 feet

Height of the cone (h) = 8 feet

Volume of the cone (V) = ?

We know that, volume of a conical shape of radius 'r' and height 'h' is given as:

$V=\frac{1}{3}\pi r^2h$

Now, plug in the given values and use 3.14 for π. Solve for 'V'. This gives,

$V=\frac{1}{3}\times 3.14\times 9^2\times 8\\\\V=\frac{3.14\times 81\times 8}{3}\\\\V=3.14\times 27\times 8\\\\V=678.24\ ft^3$

Therefore, the volume of the gravel of pile is 678.24 cubic feet.

8 0

3 years ago

for breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she selects a break

Mekhanik [1.2K]

I think she is wrong because she can choose each one equally. Imagine it being a spinner with 4 equal sections each one can be chosen at te same rate.

5 0

3 years ago