Solve any maths problem

Equations, derivatives, integrals, matrices, triangles, primes, statistics, or a word problem the tutor breaks into parts.

Calculus · Limits

Limit of x^n as n → oo

\lim_{n \to \infty} x^{n}

Step by step

  1. \lim_{n \to \infty^+-} x^{n}

    Try direct substitution first.

  2. \

    As x grows without bound, compare the fastest-growing terms (or divide top and bottom by the highest power).

  3. = e^{\infty \operatorname{sign}{\left(\log{\left(x \right)} \right)}}

    Take the limit.

Reveal the answer
e^{\infty \operatorname{sign}{\left(\log{\left(x \right)} \right)}}