Question

lim x стремящийся к 4, -х^-16/х^+x-20 помогите найти предел ( х во второй степени)

Answer 1

lim x⇒4 (x²-16)/(x²+x-20)= 0/0 = lim x⇒4 (x-4)*(x+4)/(x-4)*(x+5) = lim x⇒4 (x+4)/(x+5) = (4+4)/(4+5) = 8/9

 

 

x-4 сокрашается 

Answer 2

Calculation of the Limit

To find the limit of the function f(x) = (x^2 - 16)/(x^2 + x - 20) as x approaches 4, we can substitute x = 4 into the function and evaluate it. Let's calculate it step by step:

Step 1: Substitute x = 4 into the function: ``` f(4) = (4^2 - 16)/(4^2 + 4 - 20) = (16 - 16)/(16 + 4 - 20) = 0/0 ```

Step 2: Simplify the expression: ``` 0/0 ```

At this point, we have an indeterminate form of 0/0, which means we cannot determine the limit of the function just by substituting the value of x. We need to apply further algebraic manipulation or use other techniques to find the limit.

Unfortunately, the search results provided by You.com do not contain the specific information needed to solve this limit problem. However, we can try to simplify the expression by factoring the numerator and denominator and canceling out common factors.

Let's factor the numerator and denominator and see if we can simplify the expression:

f(x) = (x^2 - 16)/(x^2 + x - 20)
     = [(x - 4)(x + 4)]/[(x - 4)(x + 5)]

Step 3: Cancel out the common factor of (x - 4): ``` f(x) = (x + 4)/(x + 5) ```

Now, we can substitute x = 4 into the simplified expression and evaluate it:

f(4) = (4 + 4)/(4 + 5)
     = 8/9

Therefore, the limit of the function f(x) = (x^2 - 16)/(x^2 + x - 20) as x approaches 4 is 8/9.

Please note that this solution is based on algebraic manipulation and does not rely on the search results provided by You.com.