HSC Stuff > HSC Mathematics Extension 1
Mathematics Extension 1 Challenge Marathon
Empathy:
--- Quote from: jamonwindeyer on May 05, 2016, 01:47:58 pm ---Good thinking putting the solution in a spoiler, I'm going to go back and put other solutions in a spoiler as well ;D but yes, pending the Rui tick of approval, that is correct!! Nicely done! ;D
--- End quote ---
One of my friends just pointed out to me that i wasted alot of time on that, I could have just skipped everything up to the last step and solved it in 1-2 lines... lol
RuiAce:
Didn't even realise that someone actually attempted one of these questions.
For anyone's interest, the formal way to evaluate them is:
1. By considering -1≤cos(x)≤1, apply the squeeze theorem by choosing an appropriate function to multiply every side with
2. Use one application of L'Hopital's rule
3. (DOABLE) Split the limit into the limit of arctan(x) and the limit of x-n which was included in the given answer
4. (DOABLE) This is just 0 * 1/inf
conic curve:
Just in case anyone's interested feel free to try out this question
1. a. SKetch f(x)=(e^x)-4, showing clearly the points of intersection with the axes and the equations of any asymptotes
b. On the same diagram, sketch the graph of the inverse function f^-1(x), showing clearly any important features
c. Explain why the x-coordinate of any points of the intersection y=f(x) and y=f^-1(x) satisfies e^x - x - 4=0
d. Show the equation e^x - x - 4 =0 between x=0 and x=2 and use the method of 'halving by intervals' to find this root correct to the nearest whole number
Also anyone here wishing to try a few challenge circle geometry questions feel free to
relativity1:
for c) Would the answer be becuase the inverse is a reflection about the line y=x so the point of intersection is where x=y ie e^x-4=x therefore e^x-x-4=0?
RuiAce:
--- Quote from: relativity1 on July 12, 2016, 08:23:42 pm ---for c) Would the answer be becuase the inverse is a reflection about the line y=x so the point of intersection is where x=y ie e^x-4=x therefore e^x-x-4=0?
--- End quote ---
Yes.
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