It is proved by the definition of function limit that x = 0 under LIM (x → + ∞) cosx / radical How to prove it? How to write the format?

Cosx ranges from 0 to 1, and X under the root sign tends to + ∞ when LIM (x → + ∞),
0/+∞=0
1/+∞=0

1. If the real number x, y satisfies x = (root sign Y-3) + (root sign 3-y) + 2, find the value of the Y power of X. 2. If the root sign x + root sign - x is meaningful, then X 1. Know that the real number x, y satisfies x = (root sign Y-3) + (root sign 3-y) + 2, and find the value of the Y power of X 2. If the root sign x + root sign - x is meaningful, X shall meet () 3. Given | 2008-A | + root sign a-2009 = a, find the value of A-2008 4. If the real number x, y satisfies the square of (root x + 2) + (y-root 3) = 0, then the value of XY is ()

1.y-3 >=0,3-y >=0,
y=3,x=2,
2^3 = 8
2.x>=0,-x>=0,x=0
3.a-2009>=0,a>=2009
A-2008 + root sign a-2009 = a
Root a-2009 = 2008
a-2009 = 2008^2
a = 4034073
4.x+2=0,x=-2
Y = root 3
Xy = - 2 * root 3

Talk about the relationship between indefinite integral and definite integral. How do you understand that Newton Leibniz formula is called the basic theorem of calculus

Indefinite integral can be regarded as the inverse operation of derivative. The result is a family of functions
The result of definite integral is a number, and their essence is different
Definite integral was originally a method found in solving area and volume problems. It can solve such problems through the idea of limit
Definite integral and indefinite integral have nothing to do with each other
Later, Newton and Leibniz discovered the "Newton Leibniz formula". Through this formula, the problem of definite integral can be transformed into indefinite integral, and then calculated. In this way, there is a relationship between the two. The method is to first calculate the indefinite integral in the definite product, then substitute the upper and lower limits, and then subtract them to obtain the result of definite integral

[mathematics] [calculus] [indefinite integral] how to calculate the following formula Excuse me, what's the shape ∫ √(a^2-x^2)/x^4 dx How to calculate the integral of? I hope there is a general description of the steps, but I can't figure it out after trying for a long time The answer should be: -((a^2 - x^2)^(3/2)/(3 a^2 x^3))

Let x = acosx, 0

How to find the derivative of a piecewise function Is the derivative at the dividing point Let's say this question f(x)=e^2x (x≤0) =sin2x+b (x＞0) Other meetings are about how to ask at the dividing point. Please be more detailed

Continuity is not necessarily differentiable
Differentiable definite continuity
There are unilateral derivatives at the dividing point, i.e. left derivative and right derivative
At x = 0
Left derivative = 2E ^ 2x = 2
Right derivative = 2cos2x = 2 = left derivative, that is, the function is continuous at the dividing point, and there is a derivative, which is equal to 2

When calculating the derivative of the dividing point of a piecewise function, under what circumstances can we use the definition to obtain the derivative, and under what circumstances can we use the derivation rule to obtain the derivative?

When discussing the differentiability of piecewise function at the dividing point, it must be judged by the definition of left and right derivatives
When calculating the derivative of a piecewise function, except that the derivative at the dividing point is defined by the derivative, the other points can still be obtained according to the derivation formula of the elementary function
That's it,

It is proved by the definition of function limit that x = 0 under LIM (x → + ∞) cosx / radical How to prove it? How to write the format?