Question

Lim x>5 (3x^2-17x+10)/(x^2-25)

Answer 1

Lim(x→5) (3x²-17x+10)/(x²-25)
Возьмём производную из числителя и знаменателя одновременно:

lim(x→5) (6x-17)/(2x)=(6*5-17)/(2*5)=13/10=1,3.

Answer 2

Разложим числитель 3x^2-17x+10
D=289 - 4*3*10=289-120=169 = 13^2
x12=(17+-13)/6= 5  2/3
Получаем 3x^2-17x+10= 3(х-5)(х-2/3)=(x-5)(3x-2)
смотрим дробь (x-5)(3x-2)/(x-5)(x+5)=(3x-2)/(x+5)
Ищем lim x>5 (3x-2)/(x+5) = (3*5-2)/(5+5) = 13/10 = 1 3/10 = 1.3

Answer 3

To find the limit of the given function as x approaches 5, you can try factoring the expressions in the numerator and denominator to simplify the expression. Here's the expression:

(3x^2 - 17x + 10) / (x^2 - 25)

Let's factor both the numerator and denominator:

Numerator: 3x^2 - 17x + 10 = (3x - 2)(x - 5)

Denominator: x^2 - 25 = (x + 5)(x - 5)

Now, we can rewrite the expression as:

((3x - 2)(x - 5)) / ((x + 5)(x - 5))

Notice that we have a common factor of (x - 5) in both the numerator and denominator, which cancels out. However, you need to be careful when canceling, as x = 5 is a point where the denominator becomes zero. To handle this, we'll cancel the (x - 5) factor and then evaluate the limit:

((3x - 2)(x - 5)) / ((x + 5)(x - 5)) = (3x - 2) / (x + 5)

Now, we can find the limit as x approaches 5:

lim (x -> 5) (3x - 2) / (x + 5)

To evaluate the limit, simply plug in x = 5:

(3(5) - 2) / (5 + 5) = (15 - 2) / 10 = 13 / 10

So, the limit as x approaches 5 for the given function is 13/10.