Find the (1 / x) power of LIM e, X infinitely approaches 0

Find the (1 / x) power of LIM e, X infinitely approaches 0

The analysis is as follows: when x → - 0, 1 / X → - ∞, Lim e ^ (1 / x) = 0, when x → + 0, 1 / X → + ∞, Lim e ^ (1 / x) = + ∞, so at 0, the left and right limits are not equal, so the limit does not exist

Given that x = 12 is the solution of the equation 5A + 12x = 12 + X, find the solution of the equation AX + 2 = a (1-2x) about X

X = 12 is the solution of the equation 5A + 12x = 12 + X. & nbsp; & nbsp; substituting the value of X into 5A + 6 = 1, a = - 1, substituting a = - 1 into ax + 2 = a (1-2x) to get: - x + 2 = - (1-2x), simplifying to get: 2-x = 2x-1, the solution is: x = 1

6.05-0.32-0.68 + 2.95

6.05-0.32-0.68+2.95
=（6.05+2.95）-（0.32+0.68）
=9-1
=8

For a square with side length of 1, take 2 / 3 of the rest in turn and calculate 2 / 3 + 2 / 9 + 2 / 27 +... 2 / 3 ^ n

Finally, we take 2 / 3 ^ n and leave 1 / 3 ^ n, so the sum of the previous values equals 1-1 / 3 ^ n

It is known that 4x2-3x + 1 = a (x-1) 2 + B (x-1) + C holds for any number x, then 4A + 2B + C=

4x^2-3x+1=a(x-1)^2+b(x-1)+c
4x^2-3x+1=ax^2+(b-2a)x+a+c-b
a=4,b-2a=-3,a+c-b=1
a=4,b=5,c=2
4a+2b+c=28

(1 / 3-12 / 7 + 20 / 9-30 / 11 + 42 / 13-56 / 15) × 8 / 1 × 21

Original formula = 1 / 3 * 8 * 21 + (- 7 / 12 + 9 / 20-11 / 30) * 8 * 21 + 13 / 42 * 8 * 21-15 / 56 * 8 * 21
=56-84+52-45=-21

Let the curves y = x & # 178; + ax + B and 2Y = - 1 + XY & # 179; be tangent at point (1, - 1), and find the values of parameters a and B

For the second equation, two sides of X are derived, and 2Y '= y & # 179; + x3y & # 178; y' is taken in

Given that the function f (x) = ax & # 179; + BX & # 178; + CX obtains the minimum value - 4 at the point x, so that the value range of X whose derivative f '(x) > 0 is (1,3), the analytic expression of F (x) is obtained

If f '(x) > 0, the value range of X is (1,3), then x = 1,3 is the extreme point, and the coefficient of cubic term is a

25.5 △ 3 is calculated by vertical formula

Lim x sin (1 / 2x) when x tends to infinity

=lim sin(1/2x)/(1/x)
=lim t->0+ sint/2t (t=1/2x)
=lim t->0+ cost/2
=1/2
The luobida rule is used