HKDSE Mathematics Question Review
In this post, I will offer some new question types or HKDSE.
1. Consider the Euler's numer e.
(a) Express e^x in form of Taylor series.
(b) Derive the expression of sin(x) in form of Taylor series.
(c) Prove that the expression in (a), when x=1, converges.
(d) From (b), show that when x approaches zero, sin(x)/x = 1
(e) Suggest the alternative approach from (d) by a suitable geometrical illustration.
(Hint: You should use Sandwich Theorem to accomplish (e)).
In this post, I will offer some new question types or HKDSE.
1. Consider the Euler's numer e.
(a) Express e^x in form of Taylor series.
(b) Derive the expression of sin(x) in form of Taylor series.
(c) Prove that the expression in (a), when x=1, converges.
(d) From (b), show that when x approaches zero, sin(x)/x = 1
(e) Suggest the alternative approach from (d) by a suitable geometrical illustration.
(Hint: You should use Sandwich Theorem to accomplish (e)).
In this post, I will offer some new question types for HKDSE.
typo
In this post, I will offer some new question types or HKDSE.
1. Consider the Euler's numer e.
(a) Express e^x in form of Taylor series.
(b) Derive the expression of sin(x) in form of Taylor series.
(c) Prove that the expression in (a), when x=1, converges.
(d) From (b), show that when x approaches zero, sin(x)/x = 1
(e) Suggest the alternative approach from (d) by a suitable geometrical illustration.
(Hint: You should use Sandwich Theorem to accomplish (e)).
1. Consider the Euler's nubmer e.
typo
In this post, I will offer some new question types or HKDSE.
1. Consider the Euler's numer e.
(a) Express e^x in form of Taylor series.
(b) Derive the expression of sin(x) in form of Taylor series.
(c) Prove that the expression in (a), when x=1, converges.
(d) From (b), show that when x approaches zero, sin(x)/x = 1
(e) Suggest the alternative approach from (d) by a suitable geometrical illustration.
(Hint: You should use Sandwich Theorem to accomplish (e)).
1. Consider the Euler's nubmer e.
typo
1. Consider the Euler's number e.
typo again
2. Given a cubic equation ax^3 + bx^2 + cx +d = 0.
Explain whether the roots can be 1 complex and 2 real.
Hint: Show that for 0<x<pi/2,
sin x < x < tan x