Ask question

Ask question

All categories

nikitadnepr [17]

3 years ago

13

Find the indicated quantities for y equals f (x )equals 3 x squared. (A) Simplify StartFraction f (3 plus Upper Delta x )minus

f (3 )Over Upper Delta x EndFraction . (B) What does the quantity in part (A) approach as Upper Deltax approaches 0?

1 answer:

torisob [31]3 years ago

5 0

Answer:

6x

Step-by-step explanation:

Given that a function f(x) is given as

$y=f(x) = 3x^2$

A) $f(x+ \Delta x) = 3((x+ \Delta x)^2=3(x^2+2x \Delta x+\Delta x^2)\\f(x) = 3x^2\\f(x+ \Delta x) -f(x) = 6x \Delta x +\Delta x^2$

Now divide by delta x

$\frac{f(x+ \Delta x) -f(x)}{\Delta x}\\=6x+\Delta x$

B) When delta x tends to 0, this becomes

$6x$

(NOte: This is the derivative of f(x))

You might be interested in

Rewrite the equation C = 3.59q + 54,293 as a function of q.

MAVERICK [17]

The equation, when rewritten would be written as:

q = ( c - 54293 ) / 3.59

<h3>How to rewrite the equation in order to make q the subject</h3>

C = 3.59q + 54,293

We have the equation above, what we would have to do now would be to write the equation in such a way that q would be the subject of the formula.

This would be

3.59q = C - 54,293

Next we have to divide through by the value of q

q = $\frac{C - 54293 }{3.59}$

Read more on subject of formula here: brainly.com/question/21140562

#SPJ1

7 0

2 years ago

How do i solve x/3+10=15

yaroslaw [1]

step-by-step.

x

3

+10=15

Step 1: Simplify both sides of the equation.

1

3

x+10=15

Step 2: Subtract 10 from both sides.

1

3

x+10−10=15−10

1

3

x=5

Step 3: Multiply both sides by 3.

3*(

1

3

x)=(3)*(5)

x=15

Answer:

x=15

8 0

3 years ago

Jana planted 30 tulips. A total of 2/3 of those tulips have bloomed. How many of the tulips that Jana planted have bloomed?

kumpel [21]

20 tulips. 2/3=20/30 when you multiply both the denominator and numerator by 10.

8 0

3 years ago

name the set of 6 consecutive integers starting with -3 put the set in braces and put commas between the elements of the set

melisa1 [442]

6-3=3 that is the answer ok

6 0

3 years ago

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Wha

seraphim [82]

Answer:

$\sum_{i=1}^n x_i =459$

$\sum_{i=1}^n y_i =1227$

$\sum_{i=1}^n x^2_i =24059$

$\sum_{i=1}^n y^2_i =168843$

$\sum_{i=1}^n x_i y_i =63544$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=24059-\frac{459^2}{9}=650$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=63544-\frac{459*1227}{9}=967$

And the slope would be:

$m=\frac{967}{650}=1.488$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{459}{9}=51$

$\bar y= \frac{\sum y_i}{n}=\frac{1227}{9}=136.33$

And we can find the intercept using this:

$b=\bar y -m \bar x=136.33-(1.488*51)=60.442$

So the line would be given by:

$y=1.488 x +60.442$

And then the best predicted value of y for x = 41 is:

$y=1.488*41 +60.442 =121.45$

Step-by-step explanation:

For this case we assume the following dataset given:

x: 38,41,45,48,51,53,57,61,65

y: 116,120,123,131,142,145,148,150,152

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =459$

$\sum_{i=1}^n y_i =1227$

$\sum_{i=1}^n x^2_i =24059$

$\sum_{i=1}^n y^2_i =168843$

$\sum_{i=1}^n x_i y_i =63544$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=24059-\frac{459^2}{9}=650$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=63544-\frac{459*1227}{9}=967$

And the slope would be:

$m=\frac{967}{650}=1.488$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{459}{9}=51$

$\bar y= \frac{\sum y_i}{n}=\frac{1227}{9}=136.33$

And we can find the intercept using this:

$b=\bar y -m \bar x=136.33-(1.488*51)=60.442$

So the line would be given by:

$y=1.488 x +60.442$

And then the best predicted value of y for x = 41 is:

$y=1.488*41 +60.442 =121.45$

3 0

3 years ago