Jump to content
Sign in to follow this  

Hard Maths HL Option Calc Questions

Recommended Posts

Have had some trouble solving these questions, would appreciate any assistance or suggestions on how to approach the questions. I've tried the substitution y=vx and got to a stage where I am unable to integrate 1/f(y) and then have no idea how to further proceed (for question 7).

Question 8 I just have no idea how to approach.

 

 

hardquestions.jpg

Edited by IB`NOT`ez

Share this post


Link to post
Share on other sites

7 a) To solve any separable differential equation, get expressions of one variable on the same side and integrate: N9EhR4q.png. However the target equation is a definite integral so we need to know the bounds of integration. Because (x, v) = (1, k), (e, 2) are part of the solution, then the bounds are [k, 2] for v, and [1, e] for x. So simplify HbPNHRH.png to get 1 on right hand side. 
This works by a change of variables (u-substitution) of f(v) = x and {v = 2 <=> x= e, = k <=> x = 1}. Alternatively, suppose there is y = 1 / f(v) = 1/ x and you are finding the area under the curve 2 different ways. 

I believe it was a typo and this should be sufficient to answer the problem. However, with constant k defined and function f restrained, M0gQpY2.png and replace with any continuous variable it still hold correct.  

Regardless of v or y, no assumption of y = vx is necessary for this step. 

7 b) i) Assume v = y / x
nJWwiG1.png

I am trying to get the equation in form of 7a!

Xt10RzL.png

Finally, at x = e, v = 2 and this is 7a. Here I say that it was a typo because we have f(v), not f(y).

7 b) ii) Calculator

8. Start with

sA64JhQ.png

Edited by kw0573

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Sign in to follow this  

×
×
  • Create New...