f(x)=(54x^(3/2))/(6x1/3) −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 −3 -2.5 −2 -1.5 −1 -0.5 0 0.5 1 1.5 2 2.5 3 x y
Exercício
54 x 3 2 6 x 1 3 \frac{54x^{\frac{3}{2}}}{6x\frac{1}{3}} 6 x 3 1 54 x 2 3
Solução explicada passo a passo
1
Aplicamos a regra: a b c \frac{a}{b}c b a c = c a b =\frac{ca}{b} = b c a , onde a = 1 a=1 a = 1 , b = 3 b=3 b = 3 , c = 6 c=6 c = 6 , a / b = 1 3 a/b=\frac{1}{3} a / b = 3 1 e c a / b = 6 ⋅ ( 1 3 ) x ca/b=6\cdot \left(\frac{1}{3}\right)x c a / b = 6 ⋅ ( 3 1 ) x
54 x 3 6 ⋅ 1 3 x \frac{54\sqrt{x^{3}}}{\frac{6\cdot 1}{3}x} 3 6 ⋅ 1 x 54 x 3
2
Aplicamos a regra: a b ab ab = a b =ab = ab , onde a b = 6 ⋅ 1 ab=6\cdot 1 ab = 6 ⋅ 1 , a = 6 a=6 a = 6 e b = 1 b=1 b = 1
54 x 3 6 3 x \frac{54\sqrt{x^{3}}}{\frac{6}{3}x} 3 6 x 54 x 3
3
Aplicamos a regra: a b \frac{a}{b} b a = a b =\frac{a}{b} = b a , onde a = 6 a=6 a = 6 , b = 3 b=3 b = 3 e a / b = 6 3 a/b=\frac{6}{3} a / b = 3 6
54 x 3 2 x \frac{54\sqrt{x^{3}}}{2x} 2 x 54 x 3
4
Aplicamos a regra: a n a \frac{a^n}{a} a a n = a ( n − 1 ) =a^{\left(n-1\right)} = a ( n − 1 ) , onde a n / a = 54 x 3 2 x a^n/a=\frac{54\sqrt{x^{3}}}{2x} a n / a = 2 x 54 x 3 , a n = x 3 a^n=\sqrt{x^{3}} a n = x 3 , a = x a=x a = x e n = 3 2 n=\frac{3}{2} n = 2 3
54 x 2 \frac{54\sqrt{x}}{2} 2 54 x
5
Aplicamos a regra: a b c \frac{ab}{c} c ab = a c b =\frac{a}{c}b = c a b , onde a b = 54 x ab=54\sqrt{x} ab = 54 x , a = 54 a=54 a = 54 , b = x b=\sqrt{x} b = x , c = 2 c=2 c = 2 e a b / c = 54 x 2 ab/c=\frac{54\sqrt{x}}{2} ab / c = 2 54 x
Resposta final para o problema