# Limits

## Limits Examples

Here you will learn some limits examples for better understanding of limit concepts. Example 1 : If $$\displaystyle{\lim_{x \to \infty}}$$($${x^3+1\over x^2+1}-(ax+b)$$) = 2, then find the value of a and b. Solution : $$\displaystyle{\lim_{x \to \infty}}$$($${x^3+1\over x^2+1}-(ax+b)$$) = 2 $$\implies$$ $$\displaystyle{\lim_{x \to \infty}}$$$$x^3(1-a)-bx^2-ax+(1-b)\over x^2+1$$ = 2 $$\implies$$ $$\displaystyle{\lim_{x \to \infty}}$$$$x(1-a)-b-{a\over x}+{(1-b)\over x^2}\over 1+{1\over x^2}$$ = …

## What is Squeeze Theorem – Limit of Exponential Functions

Here, you will learn what is squeeze theorem or sandwich theorem of limit and limit of exponential function with examples. Let’s begin – Squeeze Theorem (Sandwich Theorem) If f(x) $$\leq$$ g(x) $$\leq$$ h(x); $$\forall$$ x in the neighbourhood at x = a and $$\displaystyle{\lim_{x \to a}}$$ f(x) = l = $$\displaystyle{\lim_{x \to 1}}$$ h(x) then …

## How to Find Limit of Trigonometric Functions

Here, you will learn how to find limit of trigonometric functions and limits using series expansion with example. Let’s begin –  Limit of Trigonometric Functions $$\displaystyle{\lim_{x \to 0}}$$ $$sinx\over x$$ = 1 = $$\displaystyle{\lim_{x \to 0}}$$ $$tanx\over x$$ = $$\displaystyle{\lim_{x \to 0}}$$ $$tan^{-1}x\over x$$ = $$\displaystyle{\lim_{x \to 0}}$$ $$sin^{-1}x\over x$$ [where x is measured in …

## How to Solve Indeterminate Forms of Limits

Here, you will learn how to solve indeterminate forms of limits and general methods to be used to evaluate limits with examples. Let’s begin –  Indeterminate Forms of Limits $$0\over 0$$, $$\infty \over \infty$$, $$\infty – \infty$$,$$0\times \infty$$, $$1^{\infty}$$, $$0^0$$, $${\infty}^0$$ Note : (i)  Here 0, 1 are not exact, infact both are approaching to …

## Definition of Limit in Calculus – Theorem of Limit

Here, you will learn definition of limit in calculus, left hand limit, right hand limit and fundamental theorem of limit. Let’s begin – Definition of Limit in Calculus Let f(x) be defined on an open interval about ‘a’ except possibly at ‘a’ itself. If f(x) gets arbitrarily close to L(a finite number) for all x …