What is the limit as x approaches 0 of 1-(tan(3x))/x ?

The limit as x approaches 0 of 1-(tan(3x))/x is -2

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limit as x approaches 0 of 1-(tan(3x))/x

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

- 2

Solution steps

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 lim (1) - x \to 0 lim (\frac{tan ( 3 x )}{x})

x \to 0 lim (1) = 1

x \to 0 lim (\frac{tan ( 3 x )}{x}) = 3

= 1 - 3

Simplify

= - 2

x \to 4 + lim (10 - 2 x)

x \to - 2 lim (\frac{3}{( x + 2 ) ^{2}})

x \to - 6 lim (x + 4)

x \to 0 + lim (x^{2} (ln (x))^{2})

x \to 0 lim (\frac{- 2}{x ^{2}})

What is the limit as x approaches 0 of 1-(tan(3x))/x ?
The limit as x approaches 0 of 1-(tan(3x))/x is -2