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baltoist

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Hmm, it appears my previous maths was too intimidating. In that case, have some hints!

 

Questions:

 

1. Show that the gradient of the function y=sin(x) at x=2? is 1.

Hint:

 

If y=sin(x), then dy/dx=cos(x). dy/dx gives the gradient of the function at any point, so all you need to do now is substitute 2? into the equation to find the gradient at x=2?. (Keep in mind this question uses radians, not degrees.)

 

 

2. Show that the infinite series 1/2+1/4+1/8+1/16+...+1/(2n)+... (i.e. img-3094146-1-post-27784-0-84894400-1410) is equal to 1.

Hint:

 

Let s be the value of the infinite series. Then s=1/2+1/4+1/8+1/16+...

Rearrange to get s-1/2=1/4+1/8+1/16+...

See if you can express the right hand side of this equation in terms of s, and then solve the equation for s.

 

 

3. Show that the area between the function y=sin(2x+?) and the x axis from x=0 to x=3?/2 is 3 units2.

Hint:

 

The function y=sin(2x+?) intersects the x axis at x=0, x=?/2, x=? and x=3?/2. It is negative from x=0 to x=?/2, positive from x=?/2 to x=?, and negative from x=? to x=3?/2. You will need to find the definite integral of y=sin(2x+?) for each of these regions, take the absolute value of each answer, and add them together to find the area.

 

 

4. Show that the shortest distance between the lines L1 and L2 is 2, where L1=<2,1,-3>+t<2,-1,2> and L2=<2,0,1>+s<4,2,0>

Hint:

 

Choose any point on L1 (call it P) and any point on L2 (call it Q). Find the vector between these points, PQ. Then find another vector, n, which is normal to the direction of both lines (finding the cross product is an easy way to do this). The shortest distance will be equal to the scalar projection of PQ on n.

 

 

 

 

And have some more ma... Actually, I think I'll just count this time. 4!!!!


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Thanks to Pink for the lovely avatar and W.G.A. for the amazing signature!

My OCs: Aero Wind, Shadowhide, Ebony (WIP)

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