1)lim 1-cosx/x²
x→0
2) lim arctg7x(e^2x -1)
x→0
3) lim 2+∛x+2/x+10
x→-10
4) lim x²-5x+6/x²-12x+20
x→2

Предыдущий
вопрос Следующий
вопрос

1) To find the limit as x approaches 0 of (1-cosx)/x^2:
(1-cosx)/x^2 = (1-(1-(x^2)/2!+...))/x^2
= x^2/2!x^2 + higher order terms
= 1/2 + higher order terms
As x approaches 0, the higher order terms become negligible and the limit is 1/2.

2) To find the limit as x approaches 0 of arctg(7x)(e^(2x) - 1):
As x approaches 0, the arctan(7x) approaches 0 and e^(2x) - 1 approaches 0. Therefore, the limit is 0.

3) To find the limit as x approaches -10 of (2+∛x+2)/(x+10):
As x approaches -10, the numerator approaches 2+∛2 and the denominator approaches 0. Therefore, the limit is undefined.

4) To find the limit as x approaches 2 of (x^2 - 5x + 6)/(x^2 - 12x + 20):
Factoring the numerator and denominator, we get:
(x^2 + x - 6)/(x^2 - 10x - 2x + 20)
= (x+3)(x-2)/(x-10)(x-2)
= (x+3)/(x-10)
As x approaches 2, the limit is (2+3)/(2-10) = 5/-8 = -5/8.