Error is TSFX 2010?

[Mao]

@Brightsky, ,

In this case of , we use , which yields

[brightsky]

Ahh, so x is not the time?    ...I should get used to these pronumerals.

[Chavi]

@Brightsky, ,

In this case of , we use , which yields

What is the purpose of this flowery notation?

[jasoN-]

nope, x is the position

How would you do this question from the same exam? (if my memory serves correctly)

A function y=f(x) has a tangent at point A(x, y) which crosses the x-axis at coordinate (x-1/2, 0)
The function has a y-intercept at coordinate (0, 1/e)
Find the equation of the curve.

Chavi can you confirm this question please

[Chavi]

nope, x is the position

How would you do this question from the same exam? (if my memory serves correctly)

A function y=f(x) has a tangent at point A(x, y) which crosses the x-axis at coordinate (x-1/2, 0)
The function has a y-intercept at coordinate (0, 1/e)
Find the equation of the curve.

Chavi can you confirm this question please

Hey , I did this question - it is tricky, but once you understand what you're asking for it's pretty simple.

OK, so you have points A(x,y) and (x-1/2, 0) - for the tangent to the curve - (don't confuse the y incpt of the function with the tangent to the curve)

then, find the gradient of the tangent by rise/run: dy/dx = y/(x-(x/1/2)) = 2y and thus, dx/dy = 1/2y

From this, x = (ln(y))/2 + c and at the y intercept, x=0 and y = 1/e

so you have 0 = 1/2(-1) + c, and c = 1/2

So, y = e^(2x-1)

Hint: Draw a diagram.

[Mao]

@Brightsky, ,

In this case of , we use , which yields

What is the purpose of this flowery notation?

A subtle point I am trying to push, that these kind of questions should be solved with definite integrals rather than indefinite integrals.

[jasoN-]

Oh that's awesome, thanks Chavi wasn't as hard as I thought.