lim(x->∏)sin(3x)/tan(5x) I'm 3 / 5, and the answer is - 3 / 5

lim(x->∏)sin(3x)/tan(5x) I'm 3 / 5, and the answer is - 3 / 5

According to the induction formula, sin (3x) = - sin (3x-3 Π), Tan (5x) = Tan (5x-5 Π)
When X - > Π, 3x-3 Π → 0, 5x-5 Π → 0,
Then sin (3x) is equivalent to - (3x-3 Π) and Tan (5x) is equivalent to 5x-5 Π
Original formula = lim - (3x-3 Π) / (5x-5 Π) = - 3 / 5

If x tends to infinity, find LIM (x + 3cosx) / (3x-2sinx)

lim(x+3cosx)/(3x-2sinx)=limx/3x=1/3

lim(x→1)(x^3-3x+2)/(x^3-x^2-x+1)

The original formula = LIM (x → 1) (x-1) (X-2) / [x ^ 2 (x-1) - (x-1)] = LIM (x → 1) (x-1) (X-2) / (x-1) ^ 2 (x + 1)
=LIM (x → 1) (X-2) / (x-1) (x + 1) = infinity

Let the function FX = ax-a / x-2lnx. 1. FX has extremum when x = 2. Find the value of real number a and the maximum value of FX

It is known that the square of parabola y = - x + 2 (M + 1) x + M-3 and X-axis intersect at two points AB, a is on the right side of B, and OA / ob = 3 / 1, then M=
A. B is on both sides of the origin

m=-5/3
Since there are two points of intersection between the parabola and the x-axis, there should be
If △ = B ^ 2-4ac = 4 (M + 1) ^ 2 + 4 (M + 3) = 4 (m ^ 2 + 3M + 4) > 0, Zhiheng holds
Because point a is on the left side of point B, and OA: OB = 3:1
There are two situations
(1) When points a and B are to the left of point O:
Let the coordinates of point B be B (B, 0), then the coordinates of point a are a (3b, 0), B0
The relationship between root and coefficient is as follows
b-3b = 2(m+1)
Namely - B = m + 1 (1)
b*(-3b) = -(m+3)
That is, 3b ^ 2 = m + 3 (2)
Simultaneous (1) and (2) are solved
B = - 1, M = 0
or
b=2/3 ,m=-5/3
To sum up, I know
M = 0
or
m=-5/3

First simplify, then evaluate: A's square B - (2Ab's Square - 2A's square B + 1) + (- 3A's square B + 1), where a = 4, B = - 1 / 2

Square B of a - (square of 2Ab - square B + 1 of 2a) + - square B + 1 of 3A
=The square of a the square of b-2ab + the square of 2A the square of b-1-3a B + 1
=A's square B + 2A's Square B-3A's Square b-2ab's Square-1 + 1
=-The square of 2Ab
=-Square of 2 * 4 * (- 1 / 2)
=-8*1/4
=-2

If the parameter equation of the space curve is x = a (T), y = B (T), z = (T), then,
So what are the tangent equation and normal plane equation at point m (x0, Y0, Z0)

This problem should be short of a small premise: m is on the space curve, and corresponds to the parameter t = t0
There is also a lack of Z = C (T)
Point m corresponds to the tangent equation of the curve at point M
(x-x0)/a′(t0)=(y-y0)/b′(t0)=(z-z0)/c′(t0)
The equation of hair plane is as follows
(x-x0)a′(t0)+(y-y0)b′(t0)+(z-z0)c′(t0)=0

Speed! Factorization
The square of (x + y) times (X-Y) - (x + y) times (the square of X + the square of Y)

The original formula = (x + y) [(x + y) (X-Y) - (X & # 178; + Y & # 178;)]
=(x+y)(x²-y²-x²-y²)
=-2y²(x+y)

If the coordinates of the three fixed points of the parallelogram ABCD are a (1,0) B (5,8), C (7, - 4), find the coordinates of the fourth vertex D
Please use the judgment of two straight lines parallel and vertical to describe the detailed solution process

∵AB∥CD,AD∥BC
The slopes of AB and CD are equal, KCD = (8-0) / (5-1) = 2
The slopes of AD and BC are equal, kad = (8 + 4) / (5-7) = - 6
The ad linear equation: y-0 = - 6 (x-1), y = - 6x + 6 （1）
CD linear equation: y + 4 = 2 (X-7), y = 2x-18 （2）
(1) and (2) - 6x + 6 = 2x-18
x=3
y=-12
Ψ D coordinate (3, - 12)

For (X & # 178; - 1) / (2x & # 178; - x-1), X tends to the limit of 4

5/9