Question

Помогите срочно!!! Множество преобразованных функций f(x)=(x^2-3x+4)/(x(sqrt x)) Какой Имеет вид... ???

Answer 1

Надо найти неопределенный интеграл
$\int\limits {x^n} \, dx=(x^(n+1))/n+1$
перепишем функцию
$(x^2-3x+4)/(x \sqrt{x} )=1/(x \sqrt{x} )*(x^2-3x+4)=$=$\sqrt{x} -3/ \sqrt{x} +4/ x^{3/2}$
берем интеграл почленно
$\int\limits{ \sqrt{x} } \, dx =(2* x^{3/2}) /3$$\int\limits{-3/ \sqrt{x} } \, dx = -3 \int\limits{1/ \sqrt{x} } \, dx = -3*2 \sqrt{x} =-6 \sqrt{x}$$\int\limits {4/ x^{3/2} } \, dx =4 \int\limits {1/ x^{3/2} } \, dx =4*(-2/ \sqrt{x} )= -8/ \sqrt{x}$
общий интеграл получится путем сложения интегралов + cons
$\int\limits{(x^2-3x+4)/ x^{2} } \, dx =2 x^{3/2} /3-6 \sqrt{x} =8/ \sqrt{x} +C$

Answer 2

Function Transformation

The given function is a transformed function of the form f(x) = (x^2 - 3x + 4) / (x(sqrt(x)). This type of function represents a rational function with a square root in the denominator.

Rational Function with Square Root in the Denominator

The function f(x) can be classified as a rational function with a square root in the denominator. This type of function often involves techniques such as finding the domain, asymptotes, and intercepts, and analyzing the behavior of the function as x approaches positive or negative infinity.

Further Analysis

To provide a more detailed response, it would be helpful to know the specific aspect of the function you need assistance with. For example, are you looking to find the domain and range of the function, its asymptotic behavior, or any specific points of interest on the graph of the function? Feel free to provide more details so I can tailor the response to your needs.