## Limit formula

Limits are defined in mathematics as the values at which a function approaches the output of the input data values.

Limits are essential in calculus and numerical modeling because they define integrals, variants, as well as continuity. Often used in the data analysis but always refers to the behavior of the function at a specific point.

The limit of a sequence has been further generalized in the notion of the limit of a geometrical net and is connected to the limit but instead direct constrain in the theoretical category.

In general, numerical methods are divided into two types: definite as well as indefinite integrals.

The minimum and maximum limits of definite integrals are correctly defined.

Indefinite integrals, on the other hand, are conveyed without limit values and would have an arbitrarily chosen constant whereas integrating the component.

A limit function can reach two distinct limits. One in which the variable views its limit by using values greater than its limit, and another in which the variable approaches the limit by using values less than the limit. The limit is also not outlined in this case, however, the side limits exist.

## Here are Some Important Limits Formula

Limx→0 sin x = 0

Limx→0 cos x = 1

sinxx=1

log 1+x x=1

x =1

x =1

ex-1x=1

ax-1x=a

### SOLVED EXAMPLES

Question 1. Find out the value of the given limit function: limx→2 (2x3 + 5X – 1 – 3X2)

So the given function is = Limx→2 (2x3 + 5X – 1 – 3X2 )

=Limx→2 (2x3) – Limx→2(5X) – Limx→2 (1) – LimX→2(3X2)

Or, 2 ×Limx→2 (x3) – 5 × Limx→2(X) – (1) – 3×LimX→2(X2)

=2(2)3 – 3(2)2 +5(2) -1

= 16 – (3 x 4) + 10 – 1

= 16 – 12 + 9

= 4+9

= 13

Question 2. Find out the value of the given limit function: Limx→3 (3x3 + 5X – 1 – 3X2)

So, the given function is = Limx→2 (3x3 + 5X – 1 – 3X2)

=Limx→3 (3x3) – Limx→3(5X) – Limx→3 (1) – LimX→3(3X2)

Or, 3 ×Limx→3 (x3) – 5 × Limx→3(X) – (1) – 3×LimX→3(X2)

=3(3)3 – 3(3)2 +5(3) -1

= 81 – (3 x 9) + 15 – 1

= 81 – 27 + 9

= 54+9

= 63