#continuity

Integral Calculus 2

If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is _0^a f( x )g(

Applying the basic concept, complete solution: write formula, plug data, do arithmetic. Final value matches _0^a f( x )dx. Simple and accurate.

Ref: NCERT Mathematics Class XII — Integrals

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General Mathematics 1

If f( x ) = array*20c 1 + x&if;x < 0 ( 1 - x )( px + q )&if;x 0 array .

The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as (2, 1). Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 1

The function f(x) is defined by f( x ) = array*20c | x |x 0, arrayarray*20c ,x 0 x = 0 array . then, at x = 0 it is

Let's break it down: solving fully: apply relevant formula, put numbers, compute. Result comes as Discontinuous at x = 0 and has discontinuity of first kind. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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Matrices and Determinants 3

If f(x) = matrix xx - 1 & if x 1 K & if x = 1 matrix . is continuous at x = 1, then the value of K is

Applying the basic concept, after simplifying, 1 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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General Mathematics 1

Which of the following functions is not continuous at the origin?

Recall the rule after simplifying, xx is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XI and XII

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