Mister Exam

Lang:

Limit of the function 2xsin(5*x)/5

You have entered [src]

     /2*x*sin(5*x)\
 lim |------------|
x->0+\     5      /

\lim_{x \to 0^+}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right)

Limit(((2*x)*sin(5*x))/5, x, 0)

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]

     /2*x*sin(5*x)\
 lim |------------|
x->0+\     5      /

\lim_{x \to 0^+}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right)

0

= -5.34536365768728e-30

     /2*x*sin(5*x)\
 lim |------------|
x->0-\     5      /

\lim_{x \to 0^-}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right)

0

= -5.34536365768728e-30

= -5.34536365768728e-30

Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to 0^-}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = 0

\lim_{x \to 0^+}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = 0

\lim_{x \to \infty}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = \left\langle -\infty, \infty\right\rangle

\lim_{x \to 1^-}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = \frac{2 \sin{\left(5 \right)}}{5}

\lim_{x \to 1^+}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = \frac{2 \sin{\left(5 \right)}}{5}

\lim_{x \to -\infty}\left(\frac{2 x \sin{\left(5 x \right)}}{5}\right) = \left\langle -\infty, \infty\right\rangle

Numerical answer [src]

-5.34536365768728e-30

-5.34536365768728e-30

The graph

Limit of the function 2*x*sin(5*x)/5