Evaluate 2/3 - 1/6 A. 1/6 B. 1 C. 1/2 D. 5/6

Derivatives concept: Exercises using the definition of derivatives: (Full development)

krok68 [10]

(A) f(x) = 7 is constant, so f(x + h) = 7, too, which makes f(x + h) - f(x) = 0. So f'(x) = 0.

(B) f(x) = 5x + 1 ==> f(x + h) = 5 (x + h) + 1 = 5x + 5h + 1

==> f(x + h) - f(x) = 5h

Then

$\displaystyle f'(x) = \lim_{h\to0}\frac{5h}h = \lim_{h\to0}5 = 5$

(C) f(x) = x ² + 3 ==> f(x + h) = (x + h)² + 3 = x ² + 2xh + h ² + 3

==> f(x + h) - f(x) = 2xh + h ²

$\implies\displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2}h = \lim_{h\to0}(2x+h) = 2x$

(D) f(x) = x ² + 4x - 1 ==> f(x + h) = (x + h)² + 4 (x + h) - 1 = x ² + 2xh + h ² + 4x + 4h - 1

==> f(x + h) - f(x) = 2xh + h ² + 4h

$\implies \displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2+4h}h = \lim_{h\to0}(2x+h+4) = 2x+4$

5 0

3 years ago

2 = − 7 4 + 1 4 x

finlep [7]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable. Exact Form: x = 38/7 Decimal Form: x = 5.428571 Mixed Number Form: x = 5 3/7

Step-by-step explanation:

5 0

4 years ago

It is 8:00 a.m. on Monday. Brendia's sister will arrive from New York at 8:00 a.m. on Wednesday. How many hours will it be befor

AlladinOne [14]

Answer:

it's answer is C 48 hours

7 0

3 years ago

Which of the following best describes the slope of the line below?

max2010maxim [7]

Answer:

It's an undefined slope

Step-by-step explanation:

Hope this helps!

3 0

3 years ago

Read 2 more answers

PLEASE HELP! 50 POINTS! Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). Which of the follow

Georgia [21]

Answer:

(15.23,41.016)

Step-by-step explanation:

WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.
$= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125$
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:
$= ((21 - 28.125)^{2} + (24 - 28.125)^{2} +(25 - 28.125)^{2} + (32 - 28.125)^{2} + (35 - 28.125)^{2} + (31 - 28.125)^{2} + (29 - 28.125)^{2} (28 - 28.125)^{2}$
$= 148.877/8 = 18.6$
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:
$= 28.125 + (1.96 *18.6)/(\sqrt{8} )$
$= 41.016$
$= 28.125 - (1.96 * 18.6)/(\sqrt{8}) = 15.23$
The confidence interval for this data set is (15.23,41.016)

5 0

2 years ago