Question

Вычислите предел функций

Answer 1

1).(x^3+64)=(x+4)(x^2-4x+16)

(x^3+64)/(x+4)=(x^2-4x+16)

lim(x—>-4)=48

2).4x^2-7x-2=4(x+(1/4))(x-2)=(4x+1)(x-2)

5x^2-9x-2=5(x+(1/5))(x-2)=(5x+1)(x-2)

(4x^2-7x-2)/(5x^2-9x-2)=(4x+1)(5x+1)

lim(x—> 2)=9/11

3).x^3-2x+6=x^3(1-(2/(x^2))+(6/(x^3)))

-3x^3+x^2=x^3(-3+(1/x))

(x^3-2x+6)/(-3x^3+x^2)=(1-(2/(x^2))+(6/(x^3)))/(-3+(1/x))

lim(x-> бесконечность)=-1/3

4).(sqrt(x+3)-3)(sqrt(x+3)+3)=x+3-9=x-6

(x^2-36)(sqrt(x+3)+3)=(sqrt(x+3)+3)(x-6)(x+6)

(sqrt(x+3)-3)(sqrt(x+3)+3)/(x^2-36)(sqrt(x+3)+3)= 1/(sqrt(x+3)+3)(x+6)

lim(x-> 6)=1/72