Question

Dada a função f(x) = $\sqrt{2x+3}$, calcule $\frac{f(x+h) - f(x)}{h}$

Answer 1

Resposta:

lim   [√[2*(x+h) +3]  - √[2*x +3] ]/h

h-->0

lim   [√[2*(x+h) +3]  - √[2*x +3] ]*[√[2*(x+h) +3]  + √[2*x +3] ]/h[√[2*(x+h) +3]  + √[2*x +3] ]

h-->0

lim   [√[2*(x+h) +3]²  - √[2*x +3]² ]/h[√[2*(x+h) +3]  + √[2*x +3] ]

h-->0

lim   [2x+2h +3 - 2*x -3 ]/h[√[2*(x+h) +3]  + √[2*x +3] ]

h-->0

lim   [2h ]/h[√[2*(x+h) +3]  + √[2*x +3] ]

h-->0

lim  2/[√[2*(x+h) +3]  + √[2*x +3] ]

h-->0

=2/[√[2*(x+0) +3]  + √[2*x +3] ]

=2/[√[2x +3]  + √[2*x +3] ]

=1/√[2x +3 ]