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(i) Let f(x) = A/(x-1) + B/(x²+9). Multiplying through by (x-1)(x²+9) we get x²+9x = A(x²+9) + B(x-1). By substituting x=1 in to eliminate B, we find that A=1 ,...

Since we’re finding the square roots of 2 + isqrt(5) then (x+iy)^2 = 2 + isqrt(5)Thereforex^2 + 2ixy - y^2 = 2 + isqrt(5)Take real and imaginary parts it followsx^2 - y^2 = 2 and 2ixy = isqrt(5)solving th...

Multiplying and dividing by complex numbers is very similar to how you have learned how to multiply and divide surds (numbers with a rational and irrational part) in GCSE and early A-Level. Take two compl...

First simplify the equation of the curve y= x^4 - 3x^3 .The gradient is the differential.To differentiate, bring down the power and take one from it.x^4 becomes 4x^3-3x^3 becomes (-3x3)= -9x^2dy/dx= 4x^3 ...

Using SUVAT equations:s = -20mu = 20sin(30) = 10m/sv = ?a = -9.8m/s^2t = ?v^2 = u^2 + 2asv = sqrt(100 + 40x9.8)= 22.2m/s