# L-Hospitalâ€™s rule

If at x = a, a function f(x) has an indeterminate value such as etc. then L-hospitalâ€™s rule can be applied.

consider two functions f(x) and Ï•(x) having value 0 at x = 0, then

If still f â€² (x) and
Ï•â€² (x) has value zero at x = a, then  and goes on.

# Mean Value Theorems

1. Rolleâ€™s theorem
If a function f (x) is continuous in a closed interval [ab] i.e.
a â‰¤ x â‰¤ b, and derivable in open interval (ab) i.e. a < x < b, and if f (a) = f (b), then there exist atleast one real c in (ab) such that f â€²(c) = 0
2. Lagrangeâ€™s first mean value theorem
If a function f (x) is continuous in closed interval [ab] and fâ€™(x) exist in open interval (a, b) then there exist atleast one value of c such that,
f â€² (c

# Standard Integration

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3. when n = 1, i.e.,
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u is first function, v is second function. To find first function out of two we follow â€˜ILATEâ€™ rule.

I-Inverse, L-Log function, A-Algebraic funtion,
T- Trignomatric function, E-Exponential function.