Integration

Differentiate sin^3 2x with respect to x and hence find cos^3 2x dx between pi/4 and 0. I got 1/3 as answer but the supposingly correct ans is 2/3.

well what answer did you get?

Next.

Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

State the value approached by the gradient as x becomes increasingly large. ans:3.

Dont really know what the equation is asking for in the later half.

i got 1/3 for the 1st qn too

Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

State the value approached by the gradient as x becomes increasingly large. ans:3.

Dont really know what the equation is asking for in the later half.

Hi,

We are given that dy/dx = 3 - 1/x^2.

"x becomes increasingly large" means x comes closer to infinity. When this happens, 1/x^2 approaches zero. Thus, dy/dx goes near to 3.

Thanks!

Cheers,
Wen Shih

Differentiate sin^3 2x with respect to x and hence find cos^3 2x dx between pi/4 and 0. I got 1/3 as answer but the supposingly correct ans is 2/3.

well what answer did you get?

Next.

Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

State the value approached by the gradient as x becomes increasingly large. ans:3.

Dont really know what the equation is asking for in the later half.

1/3