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Limit of the function 2cos(2x)

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  lim   (2*cos(2*x))
   -pi              
x->----+            
    12

\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)

Limit(2*cos(2*x), x, (-pi)/12)

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

Plot the graph

One‐sided limits [src]

  lim   (2*cos(2*x))
   -pi              
x->----+            
    12

\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)

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\/ 3

\sqrt{3}

= 1.73205080756888

  lim   (2*cos(2*x))
   -pi              
x->-----            
    12

\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right)

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\/ 3

\sqrt{3}

= 1.73205080756888

= 1.73205080756888

Rapid solution [src]

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\/ 3

\sqrt{3}

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}

\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}

\lim_{x \to \infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle

\lim_{x \to 0^-}\left(2 \cos{\left(2 x \right)}\right) = 2

\lim_{x \to 0^+}\left(2 \cos{\left(2 x \right)}\right) = 2

\lim_{x \to 1^-}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}

\lim_{x \to 1^+}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}

\lim_{x \to -\infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle

Numerical answer [src]

1.73205080756888

1.73205080756888

The graph

Limit of the function 2*cos(2*x)