Question

1) lim x стремиться к 3 4 x^2-11x-3/ x-3 2) lim x стремиться к бесконечностью 2/ 3x^2-4x 3) lim x стремиться к 2 x^3-1/x-1 4) lim x стремиться к -3 x^3+27/ x^2-3x +9 5) lim x стремиться к бесконечностью 2 x^2-1/ 4-7x^2 6) lim x стремиться к -1 7x - x ^2 / x ^3+1 7) lim x стремиться к 0 2/ x ^3 -2x 8) lim x стремиться к 3 x^2-5x+6/3x^2 - 9x 9) lim x стремиться к бесконечностью 10/ 3x ^2 - x 10) lim 7x^3 + 2 x ^2 -1/ 8x^3-3x +4 11) lim x стремиться к 1 x^2-1/ x^3-1 12) lim x стремиться к 5 25-x ^2/ x^3 -125 13) lim x стремиться к 2 x ^3+8/ x+2 14) lim x стремиться к 4 x ^2 - 2x -8/ 2x ^2 - 4x +4 15) lim x стремиться к 8 x^4/2x^4

Answer 1

Чувак скажи что этот знак ^ означает ну может и ответ дам

Answer 2

1. To find the limit of (4x^2 - 11x - 3) / (x - 3) as x approaches 3, we can directly substitute the value of x into the expression since it does not result in an indeterminate form: (4(3)^2 - 11(3) - 3) / (3 - 3) = (36 - 33 - 3) / 0 = 0 / 0

The expression evaluates to an indeterminate form of 0/0, which means we need to apply further algebraic manipulation or techniques like L'Hôpital's rule to evaluate the limit accurately.

2. To find the limit of 2 / (3x^2 - 4x) as x approaches infinity, we need to analyze the behavior of the expression as x becomes larger and larger: As x approaches infinity, the terms with lower powers of x become insignificant compared to the highest power of x (x^2 in this case). Therefore, we can ignore the terms 4x as x approaches infinity. The expression simplifies to: 2 / (3x^2) As x approaches infinity, the value of the expression approaches 0: lim (x → ∞) 2 / (3x^2) = 0

3. To find the limit of (x^3 - 1) / (x - 1) as x approaches 2, we can again directly substitute the value of x into the expression: (2^3 - 1) / (2 - 1) = (8 - 1) / 1 = 7 / 1 = 7

The limit evaluates to 7.

4. To find the limit of (x^3 + 27) / (x^2 - 3x + 9) as x approaches -3, we can substitute the value of x into the expression: ((-3)^3 + 27) / ((-3)^2 - 3(-3) + 9) = (-27 + 27) / (9 + 9 + 9) = 0 / 27 = 0

The limit evaluates to 0.

5. To find the limit of (2x^2 - 1) / (4 - 7x^2) as x approaches infinity, we need to analyze the behavior of the expression as x becomes larger and larger: As x approaches infinity, the terms with lower powers of x become insignificant compared to the highest power of x (x^2 in this case). Therefore, we can ignore the terms -1 and 4 as x approaches infinity. The expression simplifies to: (2x^2) / (-7x^2) As x approaches infinity, the value of the expression approaches -2/7: lim (x → ∞) (2x^2) / (-7x^2) = -2/7

6. To find the limit of (7x - x^2) / (x^3 + 1) as x approaches -1, we can substitute the value of x into the expression: (7(-1) - (-1)^2) / ((-1)^3 + 1) = (-7 - 1) / (-1 + 1) = -8 / 0

The expression evaluates to an indeterminate form of -8/0, which means we need to apply further algebraic manipulation or techniques like L'Hôpital's rule to evaluate the limit accurately.

7. To find the limit of 2 / (x^3 - 2x)