What is the limit as x approaches 0 of (2sec(x))/(csc(x)) ?

The limit as x approaches 0 of (2sec(x))/(csc(x)) is 0

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limit as x approaches 0 of (2sec(x))/(csc(x))

x \to 0 lim (\frac{2 sec ( x )}{csc ( x )})

0

Solution steps

x \to 0 lim (\frac{2 sec ( x )}{csc ( x )})

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

= 2 \cdot x \to 0 lim (\frac{sec ( x )}{csc ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 2 \cdot \frac{lim _{x \to 0} ( sec ( x ) )}{lim _{x \to 0} ( csc ( x ) )}

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

x \to 0 lim (csc (x)) = \infty

= 2 \cdot \frac{1}{\infty}

Simplify

2 \cdot \frac{1}{\infty} : 0

= 0

z \to 0 lim (\frac{1}{sin ( z )})

t \to 0 lim (- e^{t})

x \to 0 lim (\frac{sin ( h ) ( x )}{x})

x \to 0 lim (\frac{x}{10000})

x \to 0 lim (x^{2} - 5 x + 6)

What is the limit as x approaches 0 of (2sec(x))/(csc(x)) ?
The limit as x approaches 0 of (2sec(x))/(csc(x)) is 0