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MTH621 CURRENT FINALTERM PAPER 2022

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Mth621

Intermediate value theorem.

Generalized mean value theorem.

One sided derivative find krna tha ak function ka.

Prove that every bounded function is integrable.

Prove that f(x)=1+x is integrable.

Mcqs quiz files ma sa thy sary.

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MTH621 Quiz 3 Solution + Final

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Mcq sary maga file waly subjective 90% file sa he aya tha

Meanvalue theorm state 2number

Meanvalue theorm prove 5 number

Find f/g 3 number

Example dani the sinx/x ke 2 number

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Mth621

Short 2 marks

- define Lipschitz continuity

- check continuity at x=0 f(x)=x+1,x>0

f(x)=x-1,x<0

Short 3 marks

- statement of change of variable theorem

- write an example of f and g is discontinuous at x=xo but f+g is continuous at x=xo.

Long 5 marks

- prove if f is monotonic at [a,b] then f is intergrable on [a,b]

- find continuity of fog

f(x)=√x

g(x)=9-x2/x+1

MCQs from quiz 2 and 3 ur past sy and definition of mean value theorem ,piece wiss theorem and 3 theorem tha

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