$\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{x^n-a^n}{x-a} \,=\, n.a^{n-1}}$

$x$ is a variable, $a$ and $n$ are constants. The quotient of difference of $n$-th powers of $x$ and $a$ by the difference of $x$ and $a$ is often appeared in calculus as $x$ approaches $a$. So, a special limit rule for this algebraic function is developed in calculus for evaluating the limit of these types of functions.

$\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{x^n-a^n}{x-a}}$

Learn how to prove the limit of ratio of difference of $n$-th powers of $x$ and $a$ to difference of $x$ and $a$ is equal to $n$ times $a$ is raised to the power of $n-1$ in calculus.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.