Soal Matematika Limit Trigonometri.

lim x-->0 {√(x+x²) - √x}/x√x
= lim x-->0 √x(√(1+x) - 1) / x√x
= lim x -->0 (√(1+x) - 1)/x
= lim x -->0 (√(1+x) - 1)/x * (√(1+x) +1)/(√(1+x) +1)
= lim x--> 0 1+x-1 / (x * (√(1+x) +1))
= lim x-->0 x /( x * (√(1+x) +1))
= lim x--> 0 1/(√(1+x) +1)
= 1/(√1 +1) = 1/2 (D)

Lim (√(x + x^2) - √x) / x√x . (√(x + x^2) + √x)/(√(x + x^2) + √x)
= Lim (x + x^2 - x) / [x√x . (√(x(1 + x)) + √x)]
= Lim x^2 / [x√x . √x (√(1 + x) + 1)]
= Lim x^2 / [x^2 (√(1 + x) + 1)]
= Lim 1/(√(1 + x) + 1)
= 1/(√(1 + 0) + 1)
= 1/2