For your revision, students.
Suppose f(1) = f(2) = 0, f(3) = 1 and f is twice differentiable on [0,3].
for some .
Suppose f(0) = 0, f(1) = 1, f is differentiable on [0,1].
for some . (more…)
理論上，這個正整數 ，可以「要幾大，有幾大」；但實際上，我們日常接觸的運算工具，必有其限制；用 EXCEL 2003，只可以算出的最大乘階是
A F.5 student asked me the following question some days ago, reply now.
A(-3,0) and B(-1,0) are two points and P(x,y) is a variable point such that . Let C be the locus of P.
(a) Show that the equation of C is .
(b) T(a,b) is a point on C. Find the equation of the tangent to C at T.
(c) The tangent from A to C touches C at a point S in the second quadrant. Find the coordinates of S.
(d) L is a straight line which passes through point A and makes an angle with the positive -axis, where . Q(x,y) is a point on L such that . (See the figure below)
(i) Write down the coordinates of Q in terms of r and .
(ii) L cuts C at two distinct points H and K. Let , .
(1) Show that are roots of the quadratic equation .
(2) Find the range of possible values of , giving your answers correct to three significant figures.
(HKCEE 1999) (more…)
剛開三角學，同學縱使寫對公式，卻因不小心運用計算機（指的是 CASIO fx-3650P 等相關型號），以致答案出錯，太「唔抵」了。
問題一：計算 的平方 (more…)
The following theorem appears in secondary school pure mathematics textbook.
Let be an elementary function. If is well-defined, then
Fine. Then a student, chan, asked,
How about ? Is it an elementary function? (more…)
It is well-known that the following is NOT true in general,
Just give an example, let (more…)
Too busy (and meaningless) to decorate the q.e.d. blog here, just come across the following occasionally…
The drama may be interesting, no idea.
When tidying up old files, I found the following old news:
May be some vistors here know him, I guess.