Mathematics Marathon (1 Viewer)

[henry08]

A TV was purchased for $600 and was marked down 30% from its original price. Calculate its original price.

 

[tommykins]

$857

 

[bored of sc]

1) Evaluate Lim x -> 2: (2x²-x+6) / (x-2).

2) If g(x) = x⁴-x²-3 show that g(x) is an even function.

3) If y = cube root x⁵ find dy/dx.

4) (i) If f(x) = (root(x)+2) / (x-2), show that f'(x) = (-xroot(x)-4x-2root(x)) / (2x(x-2)²).
(ii) Find the equation of the tangent on the curve at x = 1.

 

[Aerath]

Not quite sure how to do 1

2. g(-x) = (-x)^4 - (-x)^2 -3 = x^4 - x^2 -3 = g(x)
Since g(x) = g(-x)
Therefore even function
3. y = x^5/3
y' = [5x^(2/3)]/3

4. I cbf reading the question, sorry

 

[bored of sc]

2. g(-x) = (-x)^4 - (-x)^2 -3 = x^4 - x^2 -3 = g(x)
Since g(x) = g(-x)
Therefore even function
3. y = x^5/3
y' = [5x^(2/3)]/3

You are correct for both questions.

 

[tommykins]

1) Evaluate Lim x -> 2: (2x²-x+6) / (x-2).

Lim x->2
4x-1/1-2 = -4x+1, x = 2
limit is -4(2)+1 = -8 + 1 = -7.

 

[bored of sc]

Lim x->2
4x-1/1-2 = -4x+1, x = 2
limit is -4(2)+1 = -8 + 1 = -7.

Correct I think. You see, I had this question in the yearly but I typed it up here wrong. The real question factorised nicely so the x-2 would cancel.

 

[lyounamu]

1) Evaluate Lim x -> 2: (2x²-x+6) / (x-2).

2) If g(x) = x⁴-x²-3 show that g(x) is an even function.

3) If y = cube root x⁵ find dy/dx.

4) (i) If f(x) = (root(x)+2) / (x-2), show that f'(x) = (-xroot(x)-4x-2root(x)) / (2x(x-2)²).
(ii) Find the equation of the tangent on the curve at x = 1.

(2x^2-x+6)/(x-2) can not be simplified though.

 

[lolokay]

Lim x->2
4x-1/1-2 = -4x+1, x = 2
limit is -4(2)+1 = -8 + 1 = -7.

is that l'hopital's? you can't apply that to the question because the denominator and numerator don't both approach 0 (I know the question was typed out wrongly). and wouldn't the -2 be cancelled out, so your limit would become +7?

 

[tommykins]

is that l'hopital's? you can't apply that to the question because the denominator and numerator don't both approach 0 (I know the question was typed out wrongly). and wouldn't the -2 be cancelled out, so your limit would become +7?

Ah crap, forgot to not involve the 2.

Evaluate Lim x -> 2: (2x²-x+6) / (x-2).
4x-1/1, x =2 so limit is 4(2) - 1 = 7.

my bad

 

[lolokay]

^well that still wouldn't work as there isn't actually a limit

 

[tommykins]

I was abit weary with that question too cause I did graph it and it just approached negative infinity

 

[Aerath]

Yeah, I was like WTF when I looked at it cause I couldn't simplify it.

 

[gibbo153]

my bad
l = 1/b²+(x+8)² + 1/b²+(x-*)²


show that dl/dx = -2p/Q where

P= [(x+8)(b²+(x-8)²)²+(x-8)(b²+(x-8)²)²]

and Q = (b²+(x=8)²)²(b²+(x-8)²)²

 

[lyounamu]

show that dl/dx = -2p/Q where

P= [(x+8)(b²+(x-8)²)²+(x-8)(b²+(x-8)²)²]

and Q = (b²+(x=8)²)²(b²+(x-8)²)²

Isn't that the past HSC question?

I remember doing that (when I practised doing past papers)

I think we need to know what l is first though.

 

[gibbo153]

Isn't that the past HSC question?

I remember doing that (when I practised doing past papers)

I think we need to know what l is first though.

i edited. yeah its from 2002 hsc =] you must have a good memory haha

 

[x.Exhaust.x]

i edited. yeah its from 2002 hsc =] you must have a good memory haha

.....What is l? Your differentiating l in respect to x. So.....

 

[bored of sc]

Simplify sinx*cosx*tanx*secx*cosec²x*cotx in terms of sinx

 

[independantz]

Simplify sinx*cosx*tanx*secx*cosec²x*cotx in terms of sinx

=cosecx, as they cancel out.

 

[shady145]

since u didnt leave a q ill leave one lol

a triangle ABC, with sides
AB=5root3
BC=5
AC=x
angle BAC=30
this triangle is not a right angled triangle
use the cosine rule to show that
x^2-15x+50=0. hence find the exact values of x.