MATH1151 HELP (2 Viewers)

[liamkk112]

shouldnt it be k^8 det(A) as when a row/column is multiplied by a scalar k then det(A) increases by a factor of k? so since its an 8x8 matrix it would be k^8?

yup ur right. idk where i got that its always k^2 lol

so final answer is 2162688 i believe then

 

[scaryshark09]

How do you do this question?

 

[ExtremelyBoredUser]

How do you do these two questions?

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Tsk tsk, naughty naughty, I saw those same questions last year

 

[scaryshark09]

Tsk tsk, naughty naughty, I saw those same questions last year

well do you know how to do them?

 

[Atheist/agnostic slayer]

Tsk tsk, naughty naughty, I saw those same questions last year

Stay in these threads.

 

[ExtremelyBoredUser]

How do you do these two questions?

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use the integral theorem where G = I = F(upper bound) - F(lower bound) and then G' = d/dx(F(..) - F(..)) and use chain rule. refer back to ur notes

 

[scaryshark09]

use the integral theorem where G = I = F(upper bound) - F(lower bound) and then G' = F'(..) - F'(..) and use chain rule. refer back to ur notes

huh? im so confused


i used this formula for the first part, but it doesn't work for the others cause of the x^2 and x^3

 

[ExtremelyBoredUser]

huh? im so confused

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i used this formula for the first part, but it doesn't work for the others cause of the x^2 and x^3

yeah cuz G = F(x^2) - F(0)

so G' = d/dx (x^2) F'(x^2) - 0*F'(0)

rest should be simple

 

[scaryshark09]

yeah cuz G = F(x^2) - F(0)

so G' = d/dx (x^2) F'(x^2) - 0*F'(0)

rest should be simple

oh okay thanks for the help

 

[ExtremelyBoredUser]

oh okay thanks for the help

np just check ur theorems from the calc booklet theyll help u solve the qs

 

[scaryshark09]

Does anyone know how to do part (ii) and (iii)??

 

[scaryshark09]

Also, does anyone know how to find a suitable g(x) for these two??

 

[liamkk112]

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Does anyone know how to do part (ii) and (iii)??

multiply by A transpose inverse on the left on both sides, should work from a first glance prolly wrong but idk

 

[scaryshark09]

multiply by A transpose inverse on the left on both sides, should work from a first glance prolly wrong but idk

thanks, multiplying by A transpose on each side worked

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Also, does anyone know how to find a suitable g(x) for these two??

anyone know this?

 

[scaryshark09]

does anyone know how to do these two questions? I really would appreciate the help, thanks

 

[scaryshark09]

 

[liamkk112]

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does anyone know how to do these two questions? I really would appreciate the help, thanks

probably use the fact that integral over the domain = 1 (sum of all probabilities = 1)
so alpha = 4ln4 i think

 

[liamkk112]

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for a), make sure the derivative of the function matches up at x= 9
so n(x-9)^(n-1)sin(1/(x-9)^2) +(x-9)^n cos(1/(x-9)^2) (-2/(x-9)^3) + 2x = 0
then well n =4 is the smallest since otherwise the cos term doesn't go away cos u get something like 1/(x-9), should work

then f'(9) = 0 ? i think

then for c), i think it's also n = 4? not too sure

 

[chigurh07]

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For part (a) use the definition of a derivative at the point x = 9, so find an expression for f'(9) = lim_{x->9} ((f(x)-f(9)/(x-9)). You'll end up getting the expression lim_{x->9} ((x-9)^(n-1)*sin(1/(x-9)^2)+x+9). This limit only exists if (x-9)^(n-1) approaches 0 since sin(1/(x-9(^2)) will oscillate rapidly as x approaches 9. This means that n > 1 since (x-9)^0 = 1 as x->9, so the smallest integer is 2. For part (b), f'(9) using the limit found in part (a) is 18, since lim_{x->9} ((x-9)^(n-1)*sin(1/(x-9)^2)+x+9) = 0 + 9 + 9 = 18. For part (c) repeat the process used in part (a) and you should get n = 5

 

[chigurh07]

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does anyone know how to do these two questions? I really would appreciate the help, thanks

The sum of all probabilities is 1, so alpha*(1/4+1/4^2+1/4^3....) = 1. Using the formula for a limiting sum of a geometric series, the LHS is
alpha*(1/4)/(1-1/4) = 1/3*alpha. So alpha = 3