√122500+100/3,4=√122600/3,4=√61300/1,7
<span>Зная, что 5 < x < 8, оцените значение выражения:
а) 6х
5 < x < 8 |*6
5*6<6*x<8*6
30<6x<48
б) -10х
5 < x < 8
-8<-x<-5 |*10
-80<-10x<-50
в) х-5
5 < x < 8 |-5
5-5<x-5<8-5
0<x-5<3
г) 3х+2
5 < x < 8 |*3
15<3x<24 |+2
17<3x+2<26</span>
Решение. Способ 1<span><span>f′</span>(x)=<span><span>(<span><span>4⋅x−7 / </span><span>x2</span></span>)</span>′</span>=
</span><span>=(<span><span><span><span>(4⋅x−7)</span>′</span>⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅<span><span>(<span>x2</span>))</span>′ / </span></span><span><span>(<span>x2</span>)</span>2</span></span>=
</span><span>=<span><span><span><span>(4⋅x)</span>′</span>⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x</span><span><span>(<span>x2</span>)</span>2</span></span>=
</span><span>=<span><span>4⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x / </span><span><span>(<span>x2</span>)</span>2
</span></span></span>Ответ:<span>f′</span>(x)=<span><span>4⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x / </span><span><span>(<span>x2</span>)</span><span>2</span></span></span>
1)13,5*9,1=122,85
2)122,85*(-3,3)=-405,405
3)-405,405:(-0,00013)=3118500