[math]sin(5x)sin(2x)[/math] for 3 terms

When I tried to get the coefficients for each term I have to deriviate too long functions

For instance the first derivative was: [math]2sin(5x)cos(2x)+5sin(2x)cos(5x)[/math]So don't you have any ideas how could I compress those products and terms into fewer-term function?]]>

How do you prove that the derivative of e^x is e^x?

If you do it by first principles, you need a result ( namely the lim of (e^h-1)./h as h tends to zero is 1) and this result appears to depend on what we are trying to prove? Unless anyone can offer me another way of thinking about this limit result.

So is it a definition?]]>

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Given that f(x)= x-2 /x+2]]>

[math]2 \log_{ 3 }{ x } + x \log_{ 3 }{ (b + c) } - y ^ { 2 } = 3[/math]in a form not involving logarithm.

Solution

[math]2 \log_{ 3 }{ x } + x \log_{ 3 }{ (b + c) } - y ^ { 2 } = 3 \\
\implies[/math][math]\log_{ 3 }{ x ^ { 2 }} + \log_{ 3 }{ (b + c )} ^ { x } - y ^ { 2 } = 3[/math]Am stucked. What do I do next?]]>I'm trying to understand how the distributive law applies to expressions involving negative numbers and how, when reading an expression, to distinguish between a negative number and a subtraction operation.

In this Khan Academy video - Difference of squares intro - the following expression is given:

[math](x + a)(x - a)[/math]

The narrator then goes on to apply [imath](x + a)[/imath] to first [imath]x[/imath], then [imath]-a[/imath].

For some reason I find this counter-intuitive.

My default way of...

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I want to try as exercice to proof the sicherman dices without using polonomials.

Are there properties I can use to proof the case with 7 as biggest number on one die and 5 as biggest number on the other die? The case with max 8 on a die I have proved taking all the cases that were relevant, but with 7 as maximum on a die it are just too much. I think there has to be an interesting propertie I can't find.

Thank you very much.

Kind Regards

Mister JWO]]>

Given a vector [imath]x = (x_1, x_2, ..., x_n)[/imath] the vector norm

[math]\max\{|2x_1 - x_2|, |x_3|, ..., |x_n|\}[/math]I verified that [imath]||x|| \geq 0, ||x|| = 0 \text{ iff } x = 0[/imath], also that [imath]||\alpha x|| = |\alpha|||x||[/imath], now I need to prove the triangle inequality, i.e. [imath]||x + y|| < ||x|| + ||y||[/imath], as the last property of a vector norm.

However, I feel like my proof is low-key incomplete. I first state that,

[math]x = (x_1, x_2, ..., x_n) \\ y = (y_1, y_2, ..., y_n) \\ x + y = (x_1 +...[/math]

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I ask about the contrary, can I find or guess what is the geometry investigation that I can use to find what create this locus only where the locus is given lonely without the description of the condition that made it.]]>

Part ii) 1/a^2 + 1/b^2 >= 8/(a+b)^2

I have completed part i) but part ii) is confusing me. My main attempt was as such:

1/a + 1/b >= 4/(a+b), using i

1/a^2 + 2/ab + 1/b^2 >= 16/(a+b)^2

1/a^2 + 1/b^2 >= 16/(a+b)^2 - 2/ab

R.T.P 16/(a+b)^2 - 2/ab >= 8/(a+b)^2

LHS - RHS = 8/(a+b)^2 -2/ab

= 4ab-2a^2-2b^2/(a+b)^2ab

but the top, by AM/GM inequality indicates that LHS - RHS <= 0, and so I gets stuck here.]]>

The sum of the values to reasonable degree of accuracy is either 3 150.745 or 3 153.755. If you take the mean, you have

[math]\frac{ 3150.745 + 3153.755 }{ 2 }= 3152.25[/math]It is stated the the sum to reasonable degree of accuracy is 3 150 to 3 sig figs. My question is how do I know the number of sig figs to round the value, if am not instructed.

The same question apply here. Is there a rule guiding the value to a reasonable...

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But I don't think it can be done.

I feel as if this question is pulling from limit laws.

Particularly, the quotient law.

If we let lim x → 5 f(x) be L and lim x → 5 f(x) = 0 be M that would mean the quotient law would be violated because M cannot equal zero.

But I don't feel like that's proof enough.

I feel as if I am missing something.

What am I...

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Answer:-

As a surface integral you have [math]f(x,y) = x^2y, curlF =\begin{vmatrix} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ y & x & -z \end{vmatrix}= [0,0,0] [/math]...

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Any advice would be appreciated, thank you.

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Good Day!

the above is from munem calculus, chapter 2 , set 2.11 and topic is "change of sign property"

It says "polynomial function f is continuous on the interval [0, 1]"

my question is how do we know from above that function is continuous on the stated interval ?

Thank you.]]>

x^5-2x^3=9

Thank you.]]>