Question

Basic theory portion and formulae in :

↪️ Continuity and Differentiability.

❌ Self Attempt.
❌No Copy / paste. ​

Answer 1

Let's revise the concept of limit.

limit:- limit of a function is it's approaching value from either side.

I,e from left or right side.

CONTINUITY:- A function say f(x) is said to be continuous if left hand limit of a function ( f(x)) is equal to right hand limit of function (f(x))is equal to the value of That function at some certain point say at x = a.

DISCONTINUOUS FUNCTION:- A function say (f(x)) is said to be DISCONTINUOUS FUNCTION if the above definition is not satisfied.

THERE ARE TWO TYPES OF DISCONTINUITES IN A FUNCTION Viz

1) REMOVABLE DISCONTINUITY.

And

2) NON REMOVABLE DISCONTINUITY.

1) REMOVABLE DISCONTINUITY:- IF L.H.L = R.H.S ≠ VALUE OF FUNCTION Then this type of discontinuity is REMOVABLE DISCONTINUITY.

THIS TYPE OF DISCONTINUITY CAN BE REMOVED BY REDEFINING THE FUNCTION AT SOME CERTAIN POINT.

2) NON-REMOVABLE DISCONTINUITY:- IF L.H.L≠R.H.S ≠VALUE OF FUNCTION THEN THIS TYPE OF DISCONTINUITY IS CALLED NON-REMOVABLE DISCONTINUITY.

THIS TYPE OF DISCONTINUITY CAN NOT BE REMOVED.

____________________________

2) DIFFERENTIABILITY :-

A FUNCTION IS SAID TO BE DIFFERENTIABLE IF L.H.D = R.H.D AT SOME CERTAIN POINT SAY AT x = A

LET THE FUNCTION IS F(X)

L.H.D=

lim F( A - H ) - F( A )

H->0 ________________

-H

R.H.D =

lim F ( A + H ) - F ( A )

H->0 ________________

H

Answer 2

Heyyy

Structurally, plant and animal cells are very similar because they are both eukaryotic cells. ... Beyond size, the main structural differences between plant and animal cells lie in a few additional structures found in plant cells. These structures include: chloroplasts, the cell wall, and vacuoles.

Anyway thats me......

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