If f (x) is not equal to 0, for any a, B, f (a + b) = f (a) * f (b), when x1. Find (1) and prove that f (x) is a subtractive function Find (2) when f (4) = 1 / 16, solve inequality f (x-3). F (5-x ^ 2)

1. F (a + b) / F (a) = f (b) let B1, f (a + b) > F (a) prove 2. F (4) = 1 / 16F (4) = f (2) * f (2) = 1 / 16F (2) equal to 1 / 4, or - 1 / 4 let a = B, f (2a) = [f (a)] ^ 2 > = 0f (a) > = 0f (2) = 1 / 4f (x-3) f (5-x ^ 2) = f (x-3 + 5-x ^ 2) = f (- x ^ 2 + X + 2) = 2x ^ 2-x

Using the continuity of the function, find the following limit LIM (x tends to 0) arctan2 ^ X / (Tan ^ 2 + (x + 2) ^ cosx)

LIM (x tends to 0) arctan2 ^ X / (TaNx ^ 2 + (x + 2) ^ cosx)
=(Pie / 4) / (0 + 2)
=Pie / 8

Let the function f (x), X belong to R, and X is not equal to 0. For any non-zero real number x, y, f (XY) = f (x) + F (y), find f (1), f (- 1)

x=1 y=1
f(xy)=f(x)+f(y) f(1)=f(1)+f(1)
f(1)=0
x=-1 y=-1
f(1)=f(-1)+f(-1)=0
f(-1)=0

Find the limit: 1) when x tends to 0 and Y tends to 1, LIM (1-xy) / (x ^ 2 + y ^ 2) 2) When x and Y tend to 0, Lim1 cos root sign (x ^ 2 + y ^ 2) / (x ^ 2 + y ^ 2); 3) When x and Y tend to 0, limx / (x + y) 2) The Lim1 cos root signs (x ^ 2 + y ^ 2) in the question are connected together and divided by (x ^ 2 + y ^ 2) at the end;

The limit of the first question is equal to 1
The limit of the second question is 1 / 2
The third topic is 1
The method of the first question X - > 0 Y - > 1 can be substituted directly
Method 1-cos root sign (x ^ 2 + y ^ 2) is equivalent to (x ^ 2 + y ^ 2) / 2
So divided by x ^ 2 + y ^ 2 equals 1 / 2
It has nothing to do with X and y
The method of question 3 y - > 0 limx - > 0 X / x = 1

Given that the function f (x) is meaningful in a neighborhood of a and X tends to a, LIM (f (x) - f (a)) / (x-a) ^ 2 = 1, then f (x) is at a ()

Move over twice to find the derivative
Limit FX derivative - 0 = 2x-2a
Xa FX increment
minimum value

Find the limit LIM (XY ^ 2) / (x ^ 2 + y ^ 4) (x, y) tends to 0

You can set y = x; Y = 2x is substituted into the limit respectively

If f (x) is not equal to 0, for any a, B, f (a + b) = f (a) * f (b), when x1. Find (1) and prove that f (x) is a subtractive function Find (2) when f (4) = 1 / 16, solve inequality f (x-3). F (5-x ^ 2)