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

The limit as x approaches 0 of 1-(tan(kx))/x is 1-k

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

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

1 - k

Solution steps

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

x \to 0 lim (1) = 1

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

= 1 - k

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