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Sergio039 [100]
2 years ago
10

(x-1)³ find derivative using definition​

Mathematics
2 answers:
Neko [114]2 years ago
5 0

Answer:

f'(x) = 3(x−1)²

Step-by-step explanation:

Definition of derivative is:

f'(x) = lim(h→0) [f(x + h) − f(x)] / h

f(x) = (x−1)³, so the derivative is:

f'(x) = lim(h→0) [(x−1+h)³ − (x−1)³] / h

f'(x) = lim(h→0) [(x−1)³ + 3(x−1)²h + 3(x−1)h² + h³ − (x−1)³] / h

f'(x) = lim(h→0) [3(x−1)²h + 3(x−1)h² + h³] / h

f'(x) = lim(h→0) [3(x−1)² + 3(x−1)h + h²]

f'(x) = 3(x−1)²

kakasveta [241]2 years ago
3 0

Step-by-step explanation:

definition of the derivative to differentiate functions. This tutorial is well understood if used with the difference quotient .

The derivative f ' of function f is defined ascthe above pic.

when this limit exists. Hence, to find the derivative from its definition, we need to find the limit of the difference quotient.

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At a store, Lauren selected a watermelon that weighed 38.4 ounces.
Mrrafil [7]

Answer:

$3.60

Step-by-step explanation:

1.50 ÷ 16 = 0.09375

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5 0
2 years ago
Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to f
STALIN [3.7K]

Answer:  b) 84

Step-by-step explanation:

Let p be the prior estimate of the required proportion.

As per given , we have

p =0.5   (The probability of getting heads on a fair coin is 0.5)

Significance level : \alpha: 1-0.90=0.10\\

Critical z-value (using z-value table ) : z_{\alpha/2}=1.645

Confidence interval width : w= 0.18

Thus , the margin of error : E=\dfrac{w}{2}=0.09

Formula to find the sample size ( if prior estimate of proportion is known.):-

n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2

Substitute the values , we get

n=0.5(1-0.5)(\dfrac{1.645}{0.09})^2

Simplify ,

n=83.5192901235\approx84  [Round of to the next whole number.]

Hence, the number of times we would have to flip the coin =<u>84</u>

hence, the correct answer is b) 84

8 0
3 years ago
3 minus a number is equal 8
krek1111 [17]

Answer

<h2>11</h2>

Step-by-step explanation:

well is you know 8+8=16 then....3-11=8

6 0
3 years ago
Help me please i only have a small amount of time
Sveta_85 [38]

Answer: 0.83

Step-by-step explanation:

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3 years ago
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In the dig ram below line l is parallel to line m. Which angles are congruent to angle 1
mixas84 [53]

Answer:

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Step-by-step explanation:

<u>The angles that are congruent to angle 1 are:  3, 8, 6</u>

<u />

Answer:  Congruent angles are 3, 8, 6

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