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The continuity of higher number function (concrete process) f(X)=1/xsinx,(x0) When we ask what the constant k is, f (x) is continuous in its domain?
When k = 1, f (x) is continuous in its domain, f (x) = 1 / xsinx, and (x0) x approaches to 0 on the right. Because sin (1 / x) is bounded, in [- 1,1], X tends to 0 and is infinitesimal. According to the limit theorem "the product of bounded function and infinitesimal is infinitesimal", i.e. limit xsin1 / x = 0, then limit f (x) = 1; f (x) = k, (x = 0
On the problem of higher numbers (continuity of functions)
arctan1/x x>0
When k =? F (x) = {is continuous at x = 0
k+e^(-x) x
lim[x->0+]arctan1/x=π/2.
lim[x->0-](k+e^(-x))=k+1.
f(0)=k+e^0=k+1.
Therefore, when K + 1 = π / 2, i.e. k = π / 2-1, f (x) is continuous at x = 0
How many liters is one cubic meter of water
One cubic meter of water equals 1000 liters
How to calculate 24 times 12 in vertical form
Evaluation of determinant X - 10.000 X - 1.00.000. X - 1 a0a1 A2.. an-1 an!
I've seen your process
Expand by column 1, determinant = (A0 + a1x + a2x ^ 2 +... + anx ^ n) * - 1 ^ (n + 1 + 1)*
If you don't understand this step, you just don't understand (n + 1 + 1)
This is the expansion theorem of determinant
Because the determinant is of order n + 1, the algebraic cofactor of the elements in the first column and row n + 1 is (- 1) ^ (n + 1 + 1) M
125 + x-125 = 100 x-160 = 270 + 90 7x = 68 + 16 find the value of X (write process)
A total of three questions, write complete
125+X-125=100
X=100
X-160=270+90
X=360+160
X=520
7X=68+16
7X=84
X=12
A barrel of oil weighs 100 kg. After half use, there are still 52 kg. How many kg does the barrel weigh?
Oil drum weight: 4kg
Half oil (excluding barrel): 100-52 = 48kg
A barrel of oil (excluding barrel): 48 * 2 = 96kg
Barrel weight: 100-96 = 4kg
Let's first look at several definitions: (1) the definition of continuous point is: if a function has a definition in a neighborhood, and if X - > X., limf (x) = f (X.), then X. is called the continuous point of F (x). A corollary is that y = f (x) is continuous at X., which is equivalent to y = f (x) is both left continuous and right continuous at X, It is also equivalent to y = f (x) at X. the left and right limits are equal to f (X.). [this includes that function continuity must satisfy three conditions at the same time: function has definition at X.; X - > X. limf (x) exists; limf (x) = f (X.) when X - > X.] elementary function is continuous in its domain of definition. (2) continuous function: function f (x) is continuous at every point in its domain of definition, According to the theorem, a function must be continuous if it is differentiable; a discontinuity must not be differentiable. Continuity is easy to judge. Let's see that there are no discontinuities in the definition and the interior (according to the above three conditions). How to judge the differentiability? Discontinuity is better than non differentiability. This is a judging method. The problem is how to judge the differentiability if it is continuous
Non differentiable functions have certain characteristics, which are generally non differentiable at a certain point. Moreover, elementary functions can be derived. Functions with absolute values may have non differentiable points, such as y = | x | where x = 0, a "cusp" appears. At this point, functions must not be differentiable
How to calculate the value of expression 4 + 5 / 6 * 7 / 8mod9?
First calculate 6 * 7 = 42, 42 / 8 = 5.25, and round to 5.5, 5 = 1.1mod9 = 1.4 + 1 = 5
Through comparison, the sentence of turbulent water in the Three Gorges is
If you have something to do, you will send emperor Bai to Jiangling at dusk
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