нужна
1.1. Знайдіть значення виразу -10 :(-1- (-3))​

Объяснение:

Пусть х км/ч-скорость по течению и у км/ч-скорость лодки против течения.

За 3 ч по течению лодка х км,за 4 ч.против течения-4у км,а вместе:

3х+4у=114 км(по условию задачи).Кроме того ,за 5 ч по течению проплыла столько же,сколько за 6ч против течения,то есть:5х=6у.То есть получаем систему уравнений:

3х+4у+114·l5l,     15x+20y=570

5х=6у ·l3l,            15x=18y,

18y+20y=570, 38y=570,y=570:38,

у=15(км/ч)-скорость лодки против течения

5х=15·6,5х=90,х=90:6,

х=18(км/ч)-скорость лодки по течению реки

First, we'll try to plug in the value:
#lim_{x to -oo}x+sqrt(x^2+2x) = -oo + sqrt(oo-oo)#
We're already encountering a problem: it is simply not allowed to have #oo-oo#, it's like dividing by zero.
We need to try a different approach.
Whenever I see this kind of limit, I try to use a trick:
#lim_{x to -oo}x+sqrt(x^2+2x)#
#= lim_{x to -oo}x+sqrt(x^2+2x)*(x-sqrt(x^2+2x))/(x-sqrt(x^2+2x))#
These are the same becaus the factor we're multiplying with is essentially #1#.
Why are we doing this? Because there exists a formula which says: #(a-b)(a+b) = a^2-b^2#
In this case #a = x# and #b = sqrt(x^2+2x)#
Let's apply this formula:
#lim_{x to -oo}(x^2-(sqrt(x^2+2x))^2)/(x-sqrt(x^2+2x))#
#= lim_{x to -oo}(x^2-x^2-2x)/(x-sqrt(x^2+2x))#
#= lim_{x to -oo}(-2x)/(x-sqrt(x^2+2x))#
Now we're going to use another trick. We'r going to use this one, because we want to get the #x^2# out of the square root:
#lim_{x to -oo}(-2x)/(x-sqrt(x^2(1+2/x))#
If you look carefully, you see it's the same thing.
Now, you might say that #sqrt(x^2) = x#, but you have to remember that #x# is a negative number. Because we're taking the positive square root, #sqrt(x^2) = -x# in this case.
#= lim_{x to -oo}(-2x)/(x+xsqrt(1+2/x))#
#= lim_{x to -oo}(-2x)/(x(1+sqrt(1+2/x)))#
We can cancel the #x#:
#= lim_{x to -oo}(-2)/(1+sqrt(1+2/x))#
And now, we can finally plug in the value:
#= -2/(1+sqrt(1+2/-oo))#
A number divided by infinity, is always #0#:
#= -2/(1+sqrt(1+0)) = -2/(1+1) = -2/2 = -1#
This is the final answer.
Hope it helps.