a) if y= x^m (1−x)^n , where n∈ Z^+ , the set of positive integers,
show that when (dy/dx)=0, x=(m/(m+n))
b)if y = 2(x−5)(√(x+4)) ,show that (dy/dx) = ((3(x+1))/((√(x+4)) ))
c) solve the equation sinx−sin5x+cos3x = 0 for 0°≤x≤180°
consider the general definite intergral
I_n =∫_0 ^(π/2) sin^n xdx
a) prove that for n≥2, nI_n =(n−1)I_(n−2) .
b) Find the values of i)∫_0 ^(π/2) sin^5 dx ii) ∫_0 ^(π/2) sin^6 dx
Given that ∣z−6∣=2∣z+6−9i∣,
a) Use algebra to show that the locus of z is a circle,
stating its center and its radius.
b) sketch the locus z on an argand diagram.
A father with 8 children takes 3 at a
time to the garden as often as he
without taking the same 3 children
together more than once. The number
of times he will go to the garden is
A father with 8 children takes 3 at a
time to the garden as often as he
without taking the same 3 children
together more than once. The number
of times he will go to the garden is