# MATH1151 HELP (1 Viewer)

#### liamkk112

##### Well-Known Member
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

##### ∞∆ who let 'em cook dis long ∆∞
How do you do this question?

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#### scaryshark09

##### ∞∆ who let 'em cook dis long ∆∞
Tsk tsk, naughty naughty, I saw those same questions last year
well do you know how to do them?

#### Atheist/agnostic slayer

##### Active Member
Tsk tsk, naughty naughty, I saw those same questions last year

#### scaryshark09

##### ∞∆ who let 'em cook dis long ∆∞
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

##### Bored Uni Student
huh? im so confused

View attachment 42817
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

##### ∞∆ who let 'em cook dis long ∆∞
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

##### Bored Uni Student
oh okay thanks for the help
np just check ur theorems from the calc booklet theyll help u solve the qs

#### scaryshark09

##### ∞∆ who let 'em cook dis long ∆∞

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

#### scaryshark09

##### ∞∆ who let 'em cook dis long ∆∞

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

#### liamkk112

##### Well-Known Member
View attachment 42890
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

##### ∞∆ who let 'em cook dis long ∆∞

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

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#### liamkk112

##### Well-Known Member
View attachment 43051

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

##### Well-Known Member
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

##### Member
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

##### Member
View attachment 43051

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