Evaluate from Mathematics Limits and Derivatives
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    Limits and Derivatives

    Multiple Choice QuestionsShort Answer Type

    21.

    Evaluate space space limit as straight x rightwards arrow straight x over 4 of fraction numerator cos space straight x space minus space sin space straight x over denominator straight x minus straight pi divided by 4 end fraction.

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    Answer
    22.

    Evaluate space space space space space limit as straight x rightwards arrow straight pi of fraction numerator sin left parenthesis straight n minus straight pi right parenthesis over denominator straight pi left parenthesis straight pi minus straight x right parenthesis end fraction.

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    23.

    Evaluate space space space space space space space space space space space space limit as straight x rightwards arrow 0 of fraction numerator sin space space ax plus bx over denominator ax plus sin space bx end fraction comma space straight a comma space space straight b comma space straight a plus straight b not equal to 0

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    24.

    Evaluate space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 0 of left parenthesis cosec space straight x minus cot space straight x right parenthesis

    space space space space space space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 0 of left parenthesis cosec space straight x space minus space cot space straight x right parenthesis space equals space limit as straight x rightwards arrow 0 of open parentheses fraction numerator 1 over denominator siin space straight x end fraction minus fraction numerator cos space straight x over denominator siin space straight x end fraction close parentheses equals limit as straight x rightwards arrow 0 of fraction numerator 1 minus cos space straight x over denominator sin space straight x end fraction equals limit as straight x rightwards arrow 0 of fraction numerator 2 sin squared begin display style straight x over 2 end style over denominator sin space straight x end fraction



          space space space space space space space space space space space space space space space space equals space 2 limit as straight x rightwards arrow 0 of fraction numerator sin begin display style straight x over 2 end style. sin begin display style straight x over 2 end style over denominator sin space straight x end fraction equals limit as straight x rightwards arrow of fraction numerator begin display style fraction numerator sinx divided by 2 over denominator straight x divided by 2 end fraction end style over denominator begin display style fraction numerator sin space straight x over denominator straight x end fraction end style end fraction. sin straight x over 2


                space space space space space space space space space space space space space equals space fraction numerator limit as begin display style straight x over 2 end style rightwards arrow 0 of begin display style fraction numerator sinx divided by 2 over denominator straight x divided by 2 end fraction end style over denominator limit as straight x rightwards arrow 0 of begin display style fraction numerator sin space straight x over denominator straight x end fraction end style end fraction. limit as straight x rightwards arrow 0 of sin straight x over 2 equals 1 over 1.0 space equals 0
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    25. Find the derivative of x2-2 at x = 10.
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    26. Find the derivative of f (x) = 7 at x = 3
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    27.

    Find the derivative of space fraction numerator 1 over denominator square root of 3 straight x plus 1 end root end fraction at x =2.

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    28. Find the derivative of the following functions from first principle. 

    (x-1) (x-2)
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    29. Find the derivative of the following functions from first principle. 

    space space space space space fraction numerator straight x plus 1 over denominator straight x minus 1 end fraction
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    Answer
    30.

    Find the derivative of f(x) = 

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