Limit of sinx/x as x approaches 0: Formula, Proof

The limit of sinx/x as x approaches 0 is 1, that is, the limit formula of sinx/x when x tends to 0 is given by limx→0 $\dfrac{\sin x}{x} = 1$. Let us now prove that the limit of sinx/x is equal to 1 when x goes to 0. Limit of sinx/x as x→0 by Sandwich or … Read more

Proofs of all Limit Properties [ε-δ Definition]

In this post, we will at first recall all the properties of the limits, and then will prove them using the epsilon-delta method. The following are some properties of limits.  Properties of Limits Let us consider two functions f(x) and g(x) of the variable x, and let $a$ be a real number. Assuming both the … Read more

Limit of a function: Definition, Formulas and Examples

In this section, we will first provide the definition of the limit of a function. Then we will list all the important limit formulas. In the end, we will learn how to use them to evaluate limits. Left-hand limit and Right-hand limit: At first, we will understand both the left-hand side and right-hand side limits … Read more

Proofs of all Limit Formulas

Some important limit formulas will be discussed here. The concept of the limit of a function is very useful in the theory of Calculus. In this post, we will prove all the important limit formulas one by one. Trigonometric Functions Limit Formulas At first, we will show that the limit of sin(x)/x is 1 when … Read more