Example of absolute limit 1. Take an example to show that | f | continuity does not mean f continuity 2. For example, function f is discontinuous everywhere, but | f | is continuous everywhere

Example of absolute limit 1. Take an example to show that | f | continuity does not mean f continuity 2. For example, function f is discontinuous everywhere, but | f | is continuous everywhere

one
f(x)
=-1 (when x0)
Obviously, f (x) is discontinuous at 0, but | f (x) | = 1 is constant, so | f (x) | is continuous
two
f(x)
=-1 (when x is a rational number)
=1 (when x is an irrational number)
F (x) is discontinuous at any point
But | f (x) | = 1 is always true, so | f (x) | is continuous at any point

Find the limit with absolute value {e ^ [- (x ^ 2 + y ^ 2) ^ - 1]} divided by the sum of the absolute values of X, y Find the upper limit X and Y close to 0 Let x = RCOs θ y=rsin θ so what?

Bring in

Given that the vertex coordinates of the parabola y = - 2x2 + BX + C are (1,2), find the values of B and C, and write the analytical formula of the function

∵ the vertex coordinates of parabola y = - 2x2 + BX + C are (1,2),
∴-b
two × (−2)=1，
The solution is b = 4,
When x = 1, - 2 + 4 + C = 2,
The solution is C = 0,
Therefore, the analytic expression of the function is y = - 2x2 + 4x

Given that the vertex coordinates of the parabola y = x * 2 + BX + C are (1,4), what is the functional relationship corresponding to this parabola?

Parabola y = x ²＋ bx＋c=(x－1) ²＋ four
Namely:
y=(x－1) ²＋ four
y=x ²－ 2x＋5

Given that the vertex coordinates of parabola y = x2 + BX + C are (1, - 3), then the values of B 'C are:

y=x2+bx+c
=(x + B / 2) ^ 2 + C-B ^ 2 / 4 (formula can also be used here to directly give vertex coordinates)
So the vertex coordinates are
（-b/2,c-b^2/4 )
Vertex coordinates are (1, - 3)
therefore
-b/2=1 c-b^2/4=-3
The solution is b = - 2 and C = - 2

Given that the vertex coordinates of the parabola y = - 2x2 + BX + C are (1,2), find the values of B and C, and write the analytical formula of the function

∵ the vertex coordinates of parabola y = - 2x2 + BX + C are (1,2),
∴-b
two × (−2)=1，
The solution is b = 4,
When x = 1, - 2 + 4 + C = 2,
The solution is C = 0,
Therefore, the analytic expression of the function is y = - 2x2 + 4x