Evaluate `lim_(xtooo) sqrt(x)(sqrt(x+c)-sqrt(x)).`

Explanation

`underset(xtooo)limsqrt(x)(sqrt(x+c)-sqrt(x)" "(oo-oo"form")`
`=underset(xtooo)lim(sqrt(x)(x+c-sqrt(x))(sqrt(x+c)+sqrt(x)))/((sqrt(x+c)+sqrt(x)))`
`=underset(xtooo)lim(sqrt(x)(x+c-x))/(sqrt(x+c)+sqrt(x))`
`=underset(xtooo)lim(csqrt(x))/(sqrt(x+c)+sqrt(x))" "("from"(oo)/(oo))`
`=underset(xtooo)lim(c)/(sqrt(1+(c)/(x)+1))" "["Dividing N' and D' by" sqrt(x)]`
`=(c)/(sqrt(1+0)+1)=(c)/(2)`