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First we calculate du/dx = -2x and rearrange to get dx as the subject, dx=du/(-2x). Now we change the limits of integration because we are now integrating with respect to u. So the bottom limit will be u(...

One helpful method for solving questions like these is to sketch the curve in stages. First begin with the straight line y=3x+4 (taking 3x+4 from within the modulus lines) crossing the x axis at -4/3 and ...

sin(A+B) ≡ sin(A)cos(B) + sin(B)cos(A)

⇒ sin(75°) = sin(30+45)° = sin(30°)cos(45°) + sin(45°)cos(30°)

= ½ × 1/√2 + 1/√2 ×(√3)/2 = 1/(2√2) + (√3)/(2√2)

= (1+√3)/(2√2)

e^x, the differential of the exponential function is itself.

Simply take B from A i = 10-3=7 j= -3-2=-5 k= 2-5=-3 SO the velocity is (7i-5j-3k)