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#1 Re: Help Me ! » math » 2018-02-13 17:40:05

What happens when x is greater than or equal to 1?

#2 Re: Help Me ! » Math » 2018-02-13 17:35:43

What is the limit of your function as x approaches 2?

#3 Re: This is Cool » the Mythical formula to calculate Numerical Derivatives! » 2018-02-12 08:14:24

These coefficients are part of a more general phenomenon called the Savitzky-Golay filter in numerical analysis. In fact the traditional five-point 'stencil' reads:

where
. You can derive this result simply by playing around with the Taylor series for
with
. It's a little tedious, but you can see the derivation here: https://en.wikipedia.org/wiki/Five-poin … he_formula

There are analogous formulae for higher order derivatives too, and several published papers about the error term.

#4 Re: Help Me ! » Calculus 1 » 2018-02-11 19:27:27

Hi Sara,

Thanks for stopping by -- have you considered registering an account with us?

Have you heard of the chain rule, i.e.
?

#5 Re: Help Me ! » Please Check My Work Regarding Limit » 2018-02-07 20:01:15

Monox D. I-Fly wrote:

So, the approximation of x doesn't have to be 0 to make it equals 1?

#6 Re: Introductions » where is bobbym? » 2018-02-04 01:09:19

Bobbym sadly left us last year. We all miss him very much. There is a thread dedicated to him here: http://www.mathisfunforum.com/viewtopic.php?id=23912

#7 Re: Help Me ! » the largest interval on the following table » 2018-02-04 01:07:40

Hannibal lecter wrote:

and the second question is : Q2)  Find the largest time interval over which the actual US consumption of biodiesel was an increasing function of time. Interpret what increasing means, practically speaking, in this case.

I found the answer is for Q2 :-

The largest time interval was 2005–2007 since the percentage growth rates were positive for each of these three consecutive years. This means that the amount of biofuels consumed in the US steadily increased during the three year span from 2005 to 2007, then decreased in 2008


that don't make any sense? the first answer of Q1 say the largest interval is from 2008-2009
and the second answer for the Q2 said that the largest interval from 2005-2007? as well as it'a a decreasing function not increasing! ( over this interleave )

Because the table refers to percentage growth. If it grew by a positive percentage in 2005, 2006 and 2007, then the biodiesel consumption was still increasing in those years, but it was just growing more slowly in 2007 compared to 2006 and 2005.

The biodiesel consumption decreased in 2008, because its percentage is negative. Then it grew a little bit in 2009, because the percentage is positive.

#8 Re: Help Me ! » the largest interval on the following table » 2018-02-04 01:04:19

Hannibal lecter wrote:

Hi,

The table shows the recent annual percent growth in US biodiesel consumption

https://preview.ibb.co/kDyByx/2018_02_04_151626.png

find largest time interval over which the percentage growth in the US consumption of biodiesel was an increasing function of time


I found the answer is :  largest interval was 2008–2009 since the percentage growth rate increased from−11.7 to 7.3
(Note that the percentage growth rate was a decreasing function of time over 2005–2007.)



but why it's not from 2005 - 2006?
which gives  237 to 186.6 , isn't that the largest interval

The key word here is that we want to find the largest time interval where the percentage growth was an increasing function of time. Imagine plotting a graph with years on the x-axis and percentage growth on the y-axis -- what would it look like?

#9 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-04 00:56:51

Ah, I see -- my apologies, I misread the original equation. In that case, you are completely correct.

#10 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 23:05:47

No, it's -1/4: the gradient of a line and the gradient of the line perpendicular to it must multiply to make -1.

#11 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 20:42:40

Yes, so if the perpendicular line has a gradient of
, then the line must be of the form
. Given that the line passes through
, can you find the value of
?

#12 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 07:59:28

Correct! And you can check your answer by substituting x = 1 into your answer to get y = 5.

Now for the perpendicular line passing through (1,5). The line y = 4x + 7 has a gradient of 4. What is the gradient of the perpendicular line?

#13 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 06:15:40

Let's start with finding the parallel line through (1,5).

Can you write down a line which is parallel to y = 4x + 7?

#14 Re: Help Me ! » important question about Volum of sphare » 2018-02-03 03:53:32

Hannibal lecter wrote:

The average velocity, v, for a trip over a fixed distance, d, is inversely proportional to the time of travel, t.

which is v= d/t

there is no a constant of proportionality here why?

There is: it's
, the fixed distance. Since the distance doesn't change, that's the 'constant of proportionality'.

#15 Re: Help Me ! » determine slope of an equation without using dervitice » 2018-02-03 02:02:28

And what is the slope of a line with equation y = mx + c?

#16 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 02:01:37

No, you need to find two lines: one which is parallel to y = 4x + 7, and one which is perpendicular to it, each of which pass through (1,5).

#17 Re: Help Me ! » a montonic funtion » 2018-02-03 00:33:11

OK, take the line
. Do you see that
?

The '≤' sign accounts for the fact that the function doesn't have to be increasing at all points.

#19 Re: Help Me ! » a montonic funtion » 2018-02-03 00:22:58

Those inequalities are essentially saying everything that we've just discussed: imagine that
and
are points on the
-axis. In fact, let's use 
and
instead.

We know that
is to the right of
on the
-axis, i.e.
. Then,
is a point on the curve, and
is a point on the curve. So if
, this means that the point corresponding to
is 'below' the point corresponding to
.

The statement
just says that for any two different points you pick, one of them is always going to be 'below' the other -- which means that it's strictly increasing.

The difference between 'strictly increasing' and 'monotonically increasing' is virtually the same as the difference between '
' and '
' -- make sense?

#20 Re: Help Me ! » question about linear function form » 2018-02-02 20:30:17

Hannibal lecter wrote:

for example,  y = 10 + mx
b = 10
what is it intercept?

The
-intercept is the point at which the line crosses the
-axis.

Since
, then the coordinates of the
-intercept are
. Or sometimes people just say that the
-intercept is
.

#21 Re: Help Me ! » [ASK] Induction Again » 2018-02-02 20:27:52

Have you come across these formulae before?

If not, then one approach (which fits the title of the thread more accurately, I suppose) is to prove this result by induction:

and then once you have, set that equal to 364 and solve.

#22 Re: Help Me ! » a montonic funtion » 2018-02-02 20:22:52

Hannibal lecter wrote:

Hi,

what is the explanation of  1) "  A function f(x) is monotonic if it increases for all x or decreases for all x.?

what is the meaning of monotonic ?

I know what is the increasing function and what is the decreasing

but what is the meaning of monotonic

and what is

2) Strictly Decreasing?
3) Strictly Increasing?

what is the meaning of Strictly ?????

First, let's examine what is meant by the word 'increasing'. How can you look at a graph and immediately tell if it is increasing or not? One way is to look at the slope (or, if you've done any calculus, the 'derivative', which tells you the slope of the function at every point). If the slope at that point is positive, then the function is increasing. If it is negative, it is decreasing. If it is 0, then it's stationary. Now let's try to understand what is meant by 'monotone'.

220px-Monotonicity_example1.png

This is an example of a function which is monotonically increasing. Notice that the graph is always 'heading upwards' (think about the tangents to this curve for a more accurate description). This happens until we get to the middle, where the graph resembles a horizontal line. It's not increasing along this part -- but it also isn't decreasing. In other words, if something is monotonically increasing, then it doesn't decrease.

220px-Monotonicity_example2.png

This is an example of a function which is monotonically decreasing. Notice that the graph is always 'heading downwards', except when we get to the horizontal part of the curve. In other words, if something is monotonically decreasing, then it doesn't increase.

220px-Monotonicity_example3.png

That's a function which isn't monotone at all -- do you see why?

As for 'strictly increasing', then this means that the function must always be increasing -- it won't have any 'horizontal parts'. Likewise for 'strictly decreasing'.

There are formal mathematical definitions for all of these terms, by the way -- but I want to make sure that you understand what the picture looks like first. Does this help?

#23 Re: Help Me ! » [ASK] Induction Again » 2018-02-02 20:03:36

Monox D. I-Fly wrote:

I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as

+
+
+ ... +
= 364.

No: this is not an arithmetic series. The terms form the sequence of triangular numbers, whose nth term is
(which you can also write as
, though I prefer the former).

You have been asked to find the value of
such that
That last term is the nth term of the sequence
. Notice that if
, then
. Similarly taking
gives you
, and so on. So what you actually want to do is find the value of
such that:

Do you know how to do that?

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