What is the limit as x approaches 0 of x^{-3}sin(3x)+x^{-2}a+b ?

The limit as x approaches 0 of x^{-3}sin(3x)+x^{-2}a+b is infinity

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limit as x approaches 0 of x^{-3}sin(3x)+x^{-2}a+b

x \to 0 lim (x^{- 3} sin (3 x) + x^{- 2} a + b)

\infty

Solution steps

x \to 0 lim (x^{- 3} sin (3 x) + x^{- 2} a + b)

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (x^{- 3} sin (3 x) + x^{- 2} a + b) = \infty

x \to 0 + lim (x^{- 3} sin (3 x) + x^{- 2} a + b) = \infty

= \infty

What is the limit as x approaches 0 of x^{-3}sin(3x)+x^{-2}a+b ?
The limit as x approaches 0 of x^{-3}sin(3x)+x^{-2}a+b is infinity