MATH1151 HELP (1 Viewer)

[Voolgdognng]

How do i convert from parametric vector form to cartesian form for a plane

 

[ExtremelyBoredUser]

How do i convert from parametric vector form to cartesian form for a plane

pre sure the conventional way is

the eq of plane is given by
l = a + tu + mv where t,m are scalars and u,a,v are vectors

Find the normal of the plane by cross producting the direction vectors so n = u x v in this case
Apply the formula,
n * (x-a) = 0 (where n is the normal, x is (x,y,z) \in R3 and a is the vector and * means dot product)
and then expand and get your cartesian equation

cbf latexing sorry

 

[Voolgdognng]

pre sure the conventional way is

the eq of plane is given by
l = a + tu + mv where t,m are scalars and u,a,v are vectors

Find the normal of the plane by cross producting the direction vectors so n = u x v in this case
Apply the formula,
n * (x-a) = 0 (where n is the normal, x is (x,y,z) \in R3 and a is the vector and * means dot product)
and then expand and get your cartesian equation

cbf latexing sorry

thanks, understood it now

 

[ExtremelyBoredUser]

np all the best, just make sure to document all this stuff bc its easy to forget maths over the weeks.

 

[Voolgdognng]

How would you go about doing this

 

[liamkk112]

View attachment 42646

How would you go about doing this

for a draw the graoh, if your solution is bounded then thats it

 

[kendricklamarlover101]

View attachment 42646

How would you go about doing this

for c) the harmonic series diverges so it is bounded above and the lower bound will just be 1

 

[Luukas.2]

View attachment 42646

How would you go about doing this

(a) is bounded above but not below as its a negative cubic, and so the region above will be or .

(b) must be bounded below as . It's also bounded above as

(c) must be bounded below as the sum is always at least 1 and it increases without bound, so there must be a largest for which the sum is under 10.

 

[scaryshark09]

Does anyone know how to do part 3 and 4?

 

[chigurh07]

Does anyone know how to do part 3 and 4?

View attachment 42690

I think you can do polynomial long division for both and keep continuing the dividing process until you have a constant in the quotient, then whatever the quotient is is your answer. So for part 3 I think it would be 4*x-9 then for part 4 you could multiply the numerator by a constant to make the division process easier then you should end up with a linear expression as the quotient after dividing, then divide the quotient by the constant you multiplied the numerator by to get the final answer

 

[liamkk112]

Does anyone know how to do part 3 and 4?

View attachment 42690

for iii), i think if u do long division u can write the rational function as (4x-9) + 16/(x+1), and 16/(x+1) is O(x^-1) so the answer should just be 4x-9

for iv) similar process, just note that x^(-2) is O(x^-1)

 

[scaryshark09]

thanks, but im confused with the 'Big O' and 'Little o' stuff

why would 16/(x+1) be O(1/x). and what does the 1/x even mean? would it be different if it was O(x)

 

[liamkk112]

thanks, but im confused with the 'Big O' and 'Little o' stuff

why would 16/(x+1) be O(1/x). and what does the 1/x even mean? would it be different if it was O(x)

dfn of O(f(x)): a function g(x) is O(f(x)) if there exists constants m and k such that for all x >=k, |g(x)|<= m|f(x)|

essentially, it means that the growth of f(x) is greater than (or equal to) the growth of g(x). clearly 16/(x+1) is O(1/x) because their growth rates are the same (or, you can find constants m and k such that the definition is satisfied, in this case k could be any number and m would be 16). similarly you can find that the result in iv) after doing long division is O(1/x).

keep in mind that g(x) being O(f(x)) just means that f(x) is an upper bound on the function. so for example, if g(x) was O(x), then it is clearly O(x^2), because x^2 grows at a greater rate than x. similarly this can be extended so if g(x) is O(x) then it is O(x^3) and so on

 

[scaryshark09]

Does anyone know how to do part c?

 

[kendricklamarlover101]

u can write det(WM^-1) as



u could also split the product up at the start to get

 

[scaryshark09]

u can write det(WM^-1) as



u could also split the product up at the start to get

lol i agree, thats what i did but it says im wrong???

 

[scaryshark09]

 

[scaryshark09]

Does anyone know what to do??

 

[liamkk112]

Does anyone know what to do??

detWM^-1
=det(-4MM^tM^-1)
=16det(M)det(M^t)det(M^-1)
=16det(MM^-1)det(M)
=16det(I)*33
=528 ?

keep in mind that det(kA) = k^2 det(A), you can check this for a 2x2 or 3x3 matrix if u like. i think that’s where the mistake is coming from

 

[kendricklamarlover101]

keep in mind that det(kA) = k^2 det(A), you can check this for a 2x2 or 3x3 matrix if u like. i think that’s where the mistake is coming from

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?