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Advanced Calculus and Function Analysis: Derivatives, Limits, and Continuity

This assignment provides solutions on derivatives, limits, and function continuity in advanced calculus.

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Advanced Calculus and Function Analysis: Derivatives,Limits, and Continuity1)Find the composite function as()()()()()()312312344fg h xfgxxffxx=++==+=+Hence, correct option isD.2)Find the derivative as()()()hchhhhhhchchh2hhhc2hc2hQQdedQdQQQQQQQQdQdQQQQQQQQddd−=−−−=−−==Hence, correct option isA.3)Find derivative of the function as42dyxdx=−When422x−=then1x=When1x=thenyis1Equation of line having slope 2 and through point()1,1is()12112221yxyxyx−=−−=−=−Hence, correct option isA.4)Find the composite function as()()92929299xgfxgxxx−=−=+=−+=Hence, correct option isA.5)For1xthe graph is a line with slope2−passing through origin and for1xthe graph isa line with slope 1.()2111xxfxxx−= +Hence, correct option isB.6)Find the derivative as

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