Question

limit

Answer 1

divide num and denum by x\[\frac{\sqrt{x^3-x^2+3x}}{\sqrt{x^3}-\sqrt{x^2}+\sqrt{3x}}=\frac{\sqrt{x-1+\frac{3}{x}}}{\sqrt{x}-1+\sqrt{\frac{3}{x}}}\]

Answer 2

note that\[\lim_{x \rightarrow \infty} \frac{3}{x}=0\]

Answer 3

what did u not understand?

Answer 4

u divided numerator and numerator by x^(3/2) ?

Answer 5

\(\large\frac{\sqrt{x^3-x^2+3x}}{\sqrt{x^3}-\sqrt{x^2}+\sqrt{3x}}=\frac{\sqrt{1-\frac{1}{x}+\frac{3}{x^2}}}{1-\sqrt{\frac{1}{x}}+\sqrt{\frac{3}{x^2}}}\)
now, 1/x and 1/x^2 will tend to 0,and final limit will tend to 1