Hello, Arun!

. . . . . 23x³ + 45x

. lim . --------------

x→∞ . .78x³ + 9

Divide numerator and denominator by x³

. . . . . 23 + 45/x² . . . . . . . 23 + 0 . . . . 23

. lim . ------------- . = . lim . --------- . = . ---

x→∞ . 78 + 9/x³ . . . .x→∞ .78 + 0 . . . . 78