Can anyone help me with this limit problem? Thanks a whole lot!

Find the limit
lim x->0 of (sin(x^2 + 2x√(x+4)) / (x^3+5x)

Use L'Hopital's rule since the limit has the form 0/0.Derive the numerator and the denominator.

d/dx[sin(x^2+2x*sqrt(x+4)]=

[cos(x^2+2x*sqrt(x+4)]*
[2x+2x/sqrt(x+4)+2sqrt(x+4)]

d/dx(x^3+5x)=3x^2+5

Then the limit is

lim x->0 of[cos(x^2+2x*sqrt(x+4)]*
[2x+2x/sqrt(x+4)+2sqrt(x+4)]/(3x^2+5)

=cos(0)[0+0+2sqrt(4)]/(0+5)

=(1)(4)/4=4/5

I had to use separate lines because when you submit it does not show the whole answer in one line.

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