A compound pendulum oscillates though a
small angle θ about its equilibrium position
such that
10a((dθ/dt))^2 = 4g cos θ , a >0 . its period is
[A] 2π(√(((5a)/(4g)) )) [B] ((2π)/5)(√(a/g)) [C] 2π(√(((2g)/(5a)) )) [D] 2π(√((5a)/g))
given that
g(x) = { ((x + 2 , if 0 ≤ x < 2)),((x^2 , if 2 ≤ x < 4)) :}
is periodic of period 4.
sketch the curve for g(x) in the interval
0≤ x < 8
evaluate g(−6).
prove or disprove(with counter−example) that
a) For all two dimensional vectors a,b,c,
a.b = a. c ⇒ b=c.
b) For all positive real numbers a,b.
((a +b)/2) ≥ (√(ab))
The graph of
y = ((a + bx)/((x−1)(x−4)))
has a turning point at P(2,−1). Find the value of a and b
and hence,sketch the curve y = f(x) showing clearly the
turning points, asympototes and intercept(s) with the
axes.
need help. When typing with microsoft word
i face some difficulties like when typing
lim_(x→0) f(x) it turns to lim_(x→0) f(x) and Σ_(r=0) ^n a_n
turns to Σ_(r=0) ^n a_n please how do i rectify this
problem? and any suggestion on a better application
to type my maths papers? thanks in advance.
Given that the function f(x) = x^3 is
differentiable in the interval (−2,2) us the mean
value theorem to find the value of x for which the
tangent to the curve is parrallel to the chord
through the points (−2,8) and (2,8).
Write down a series expansion for
ln [((1−2x)/((1+2x)^2 ))] in ascending powers of x
up to and including the term in x^4 .
if x is small that terms in x^2 and higher powers
are negleted show that (((1−2x)/(1+2x)))^(1/(2x)) ≅ (1 + x)e^(−3)
find the first 4 terms in the maclaurin[
series expansion for ln (1 + 3x) hence show that
if x^2 and higher powers of x are negleted,
then
(1 + 3x)^(3/x) = e^6 (1 −9x)