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x*atan(6*x)^(1/4)

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  • Limit of the function:
  • Limit of (1+1/x)^(2+5*x) Limit of (1+1/x)^(2+5*x)
  • Limit of (1+1/x)^3 Limit of (1+1/x)^3
  • Limit of (1+x^(-3))^(x^2) Limit of (1+x^(-3))^(x^2)
  • Limit of (x/(5+x))^(8+x) Limit of (x/(5+x))^(8+x)

  • Identical expressions

  • x*atan(six *x)^(one / four)
  • x multiply by arc tangent of gent of (6 multiply by x) to the power of (1 divide by 4)
  • x multiply by arc tangent of gent of (six multiply by x) to the power of (one divide by four)
  • x*atan(6*x)(1/4)
  • x*atan6*x1/4
  • xatan(6x)^(1/4)
  • xatan(6x)(1/4)
  • xatan6x1/4
  • xatan6x^1/4
  • x*atan(6*x)^(1 divide by 4)

  • Similar expressions

  • x*arctan(6*x)^(1/4)
Limit of the function/ x*atan(6*x)^(1/4)

Limit of the function x*atan(6*x)^(1/4)

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The solution

You have entered [src] 
     /  4 ___________\
 lim \x*\/ atan(6*x) /
x->0+
$$\lim_{x \to 0^+}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right)$$ 
Limit(x*atan(6*x)^(1/4), 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
Rapid solution [src] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
     /  4 ___________\
 lim \x*\/ atan(6*x) /
x->0+
$$\lim_{x \to 0^+}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right)$$ 
0
$$0$$ 
= 5.23566465610534e-5
     /  4 ___________\
 lim \x*\/ atan(6*x) /
x->0-
$$\lim_{x \to 0^-}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right)$$ 
0
$$0$$ 
= (-3.76365783154698e-5 - 3.76365783154698e-5j)
= (-3.76365783154698e-5 - 3.76365783154698e-5j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = \sqrt[4]{\operatorname{atan}{\left(6 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = \sqrt[4]{\operatorname{atan}{\left(6 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sqrt[4]{\operatorname{atan}{\left(6 x \right)}}\right) = - \infty \sqrt[4]{-1}$$
More at x→-oo
Numerical answer [src] 
5.23566465610534e-5
5.23566465610534e-5
The graph
Limit of the function x*atan(6*x)^(1/4)
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