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[SL]Mathematics Help


appleme

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I'm studying for a test and I came across this. I don't understand how to solve it.

huho.jpg

For a) I get as far as knowing that y=-x has to be tangent to y=1/2 x^2 + c, but I don't know how to solve that.

I think the derivative of y=1/2 x^2 + c has to be the same as the derivative of y=-x... so y=x and y=-1 so x=-1. That's where they intersect. But how do I get C? (-1,1) is where the two lines intersect... so that's a point on y= 1/2 x^2 +C. So 1= 1/2 (-1)^2 + C has to be true. So 1= 1/2 + C. C=1/2. LOL WTF I SOLVED IT

Well, does anyone know an easier way to do this?

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I can't download. But yeah, I guess it's not an IB style question.

What about this one? This one I'm actually confused about... It's in the anti-derivatives section, so it should be solvable without actual integration. It's referring to the distance, not displacement, which I don't know how to find.

blahwsj.jpg

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Ok, you cannot solve this without integration. Velocity is the variation of displacement in time:

velocity = distance/time. The derivative of distance/time (delta distance/time) results in velocity while integrating velocity results in displacement.

You know that when t = 0, the object does not move as velocity is also 0. You have to integrate the function between 2 and 0 and between 2 and 3. and add both values to solve the exercise.

1st) Integrate the function:

the integral is: 3t^2 - t^3 + c

If you integrate the function between 2 and 0:

3 (2)^2 - (2)^3 + c= 4 + c

3 (0) - (0)^3 + c = c

4 + c - c = 4.

When integrating the function between 2 and 3:

3 (2)^2 - (2)^3 + c= 4 + c

3 (3)^2 - (3)^3 + c = 0 +c

4 + c - c = 4.

Hence: 4 + 4 = 8.

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Okay I'm not sure if you guys have a copy of the May 08 Math SL mock test, but I have to do it for homework, and I don't understand what one of the questions is asking! #4 says "differentiate each of the following with respect to x" and it's like y=sin4x, y=xtanx, y=lnx/x. help please? Thanks!

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Okay I'm not sure if you guys have a copy of the May 08 Math SL mock test, but I have to do it for homework, and I don't understand what one of the questions is asking! #4 says "differentiate each of the following with respect to x" and it's like y=sin4x, y=xtanx, y=lnx/x. help please? Thanks!

Find dy/dx where y is the function.

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