Find LIM (x - > 0) x ^ 2 * sin (1 / x) / SiNx, I'm sin (1 / x) ～ 1 / x, SiNx ～ x, then LIM (x - > 0) x ^ 2 * sin (1 / x) / SiNx =lim(x->0)x^2*(1/x)/x=x/x=1 Why is the limit calculated by the pinch theorem equal to 0

Find LIM (x - > 0) x ^ 2 * sin (1 / x) / SiNx, I'm sin (1 / x) ～ 1 / x, SiNx ～ x, then LIM (x - > 0) x ^ 2 * sin (1 / x) / SiNx =lim(x->0)x^2*(1/x)/x=x/x=1 Why is the limit calculated by the pinch theorem equal to 0

The equivalent infinitesimal is wrong
Sin (1 / x) ～ 1 / X holds only when x tends to infinity
And the title of X tends to 0, 1 / X tends to infinity, we can not use the equivalent infinitesimal
lim x^2*(sin(1/x)/sinx)
=lim x/sinx * lim x*sin(1/x)
Because SiNx ~ x, and the limit of the product of infinitesimal and bounded is infinitesimal
=1*0
=0
You are welcome if you don't know

lim (x->0) sin(3x)+4x/xsec(x)

lim (x->0) sin(3x)+4x/xsec(x)
Law of lobida
=lim(x->0) (3cos(3x)+4) / (secx+xtanx*secx)
=(3+4)/(1+0)
=7

The numerator is 1 - (x) 2 and the denominator is 1 + X + (x) 2

f(x)=(1-x^2)/(1+x+x^2) df/dx=((1+x+x^2)d(1-x^2)-(1-x^2)d(1+x+x^2))/(1+x+x^2)^2=(-1-4x-x^2)dx/(1+2x+3x^2+2x^3+x^4)

Derivation Lim = (e ^ x-e ^ - x) ^ 2 numerator x-0 ln (1 + x ^ 2) denominator

=lim e^(-2x)·(e^(2x) -1)² / ln(1+x^2)
=lim e^(-2x)· lim(e^(2x) -1)² / ln(1+x^2)
=1 × LIM (2x) & # 178; / ln (1 + x ^ 2) [Equivalent Infinitesimal Substitution: e ^ X - 1 x when x → 0]
=LIM (2x) & # 178; / (x ^ 2) [Equivalent Infinitesimal Substitution: ln (1 + x) x when x → 0]
=4

3-3-1 + 99-100 + 56 = what?
One second, can you?

54. One second is not enough

Proving by Lagrange mean value theorem
Let f (x) be differentiable in the closed interval [0,1], and f (0) = 0, f (1) = 1. It is proved that for any positive number α and β with α + β = 1, there are two different points ξ and η ∈ (0,1) such that α f '(ξ) + β f' (η) = 1

There is a mean value theorem, where ξ exists such that f (α) - f (0) = α f '(ξ); where η exists such that f (1) - f (α) = (1 - α) f' (η) = β f '(η)
By adding the two formulas, α f '(ξ) + β f' (η) = f (1) - f (0) = 1

The oxygen density in the oxygen bottle of the hospital is 10kg / m3. In order to rescue the driver who is drunk and driving in a car crash, 15 of them are used, and the remaining oxygen density in the bottle is ()
A. 10kg/m3B. 2kg/m3C. 5kg/m3D. 8kg/m3

Suppose the volume of the oxygen cylinder is V, the mass of oxygen in the original oxygen cylinder is: M0 = ρ 0V, 15 of which is used, the mass of remaining oxygen is: M = 45m0 = 45 ρ 0V, ∵ the volume of oxygen in the cylinder remains unchanged, ∵ the density of remaining oxygen is: ρ = MV = 45 ρ 0vv = 45 ρ 0 = 45 × 10kg / m3 = 8kg / m3

Define a new operation a * b = (a + 1) / b. find: 2 * (3 * 4)

2*(3*4)
=2*(3+1)/4
=2*1
=2+1/1
=3

Advanced mathematics, double integral and triple integral!
Volume can be calculated by double integral and triple integral. I don't know what the difference is? Which are calculated by double integral and which are calculated by triple integral? When I see the question, how can I judge which integral should be used?
2、 What is triple integral in the end? I only know the solution and the problems in the book. I don't know what its real meaning is?
Please help me! More detailed! Explain clearly! Thank you!

You can simply solve the inverse operation of derivation. Derivation is to find the derivative of the known original function, and it is to find the original function. Double integral means that there are two unknowns and three unknowns of triple integral, and then it can be solved according to the order of integral. Some problems can be solved by double integral

Write a math diary about the length unit in grade two

Today, I learned the conversion of length unit in mathematics class. Before, I had no concept about how long a thing was. Through this lesson, I knew the length unit! At the same time, I also knew the important application of unit in real life! 1m = 100cm, don't look at such a small unit conversion, before I didn't learn, I didn't know