If the constant term in the expansion of binomial (1 / x-ax ^ 2) ^ 9 is - 21 / 2, then the real number a =? RT

If the constant term in the expansion of binomial (1 / x-ax ^ 2) ^ 9 is - 21 / 2, then the real number a =? RT

The binomial (1 / x-ax ^ 2) ^ 9 represents the multiplication of 9 (1 / x-ax ^ 2)
Out of the 9 (1 / x-ax ^ 2), take 6 (1 / x-ax ^ 2) formulas and take 1 / x, and the remaining 3 (1 / x-ax ^ 2) formulas and take ax ^ 2
Get: C (9,6) * [(1 / x) ^ 6] * (AX & # 178;) ^ 3 = - 21 / 2, a = - 1 / 2 after X is reduced

If the coefficient of x ^ 4 is 240 in the expansion of (AX-1) ^ 6, then the positive real number a =?

a^4*（6*5)/(2*1）=240
a^4=16,a=2

Let f (x) = (e ^ x) / [(x-a) (x-1)] have infinite discontinuities
X = 0 and x = 1. Try to determine the constants A and B
Let f (x) = (e ^ X-B) / [(x-a) (x-1)] have infinite discontinuities x = 0 and removable discontinuities x = 1
Sorry, everyone

1. Because when x tends to 0. F (x) is infinite. All conditions are satisfied only if the denominator is 0. Then a = 0
2. Because when x tends to 1, there is a breakpoint that can be removed. Because the denominator tends to 0 when x = 1, so the molecule should also tend to 0, otherwise there is no breakpoint. Then B = E
a=0 b=e

Analysis function discontinuity f (x) = (10 ^ x-1) / x,

Obviously, the function f (x) has only one discontinuity, x = 0 ∵ f (0 + 0) = LIM (x - > 0 +) [(10 ^ x-1) / x] = LIM (x - > 0 +) (ln10 * 10 ^ x) (0 / 0 type limit, by using Robida's law) = ln10f (0-0) = LIM (x - > 0 -) [(10 ^ x-1) / x] = LIM (x - > 0 -) (ln10 * 10 ^ x) (0 / 0 type limit, by using Robida's law) = ln10 ∵

When a takes which of the following values, the function f (x) = 2x3-9x2 + 12x-a has exactly two different zeros
A. 2B. 4C. 6D. 8

F '(x) = 6x2-18x + 12 = 6 (x-1) (X-2), we know that the possible extreme point is x = 1, x = 2, when x < 1, the function f' (x) > 0.f (x) monotonically increases; when 1 < x < 2, the function f '(x) < 0.f (x) monotonically decreases; when x > 2, the function f' (x) > 0.f (x) monotonically increases; and f (1) = 5 -

On the postgraduate entrance examination of Advanced Mathematics (using the form of function to study the number of zeros of function)
In Li Yongle's review book, we use the form of function to study the number of zeros of function
After deriving the derivative of the function, we should calculate the monotone interval and the extremum in the list step by step
But why does Li's book need to find the limits of the two ends of the interval to which the independent variable belongs before listing?
For example, when x ∈ (0, + ∞), the derivative of F (x) is obtained, and then the value of F (x) is required when x tends to 0, and the value of F (x) when x tends to + ∞ before listing
It's difficult to understand why the endpoint limit is required

Let's take an example. Let's make it simple
Suppose we find an extreme point F (1) = - 2 and f (x) is monotone on (0,1)
Then, if the limit of X tends to zero is a negative number such as - 1, then there is no zero point on (0,1)
But if the limit of X tends to zero is positive, for example, 2, then there is a zero on (0,1)
It's the same with ＋∞
Suppose you determine f (1) = - 2 and increase monotonically over (0,1)
You can't just say that there must be a zero on (1, + ∞)
Because functions can be infinitely close to zero
So find the limit where x tends to + ∞ and see if f (x) is greater than zero when x tends to infinity to determine whether there is a zero

If f (x) = {x + 1 (x0)}, then the number of zeros of the high number y = f (f (x)) + 1 is

Four

Let f (x) = | x | / x, then x = 0 is the? A removable discontinuity B infinite discontinuity C oscillating discontinuity D jumping discontinuity of F (x)

lim(x→0+)f(x)=1
lim(x→0-)f(x)=-1
D, obviously

Arctan (1 / x) does not exist at x = 0, and x = 0 is not a removable breakpoint. Can it be said that this function is not the original function to find the reciprocal of X

It should be a differentiable function, at least it is continuous in the domain

How to judge whether two functions are the same in Higher Mathematics?

Generally speaking, the forms of two functions are different. One function can be simplified to get the same form as the other function. Of course, some difficult problems are that both functions need to be simplified. To sum up, it is to satisfy the three elements of the function (domain, range and corresponding rules)