What is the limit as x approaches 0 of (tan(x))/x cos(x) ?

The limit as x approaches 0 of (tan(x))/x cos(x) is 1

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limit as x approaches 0 of (tan(x))/x cos(x)

x \to 0 lim (\frac{tan ( x )}{x} cos (x))

1

Solution steps

x \to 0 lim (\frac{tan ( x )}{x} cos (x))

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

With the exception of indeterminate form

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

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

x \to 0 lim (cos (x)) = 1

= 1 \cdot 1

Simplify

= 1

x \to \infty lim ((\frac{1 + 9}{x})^{(\frac{x}{8})})

x \to \infty lim (- \infty + ln (2))

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

x \to 0 lim (3 x)

z \to 0 lim (\frac{∣ x ∣ - z}{z})

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