Find the derivative of  at x =2. from Mathematics Limits and
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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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    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

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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.

    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 space space space space space space space space space straight f left parenthesis 2 right parenthesis space equals space space limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis 2 plus straight h right parenthesis minus straight f left parenthesis 2 right parenthesis over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator square root of 3 left parenthesis 2 plus straight h right parenthesis plus 1 end root end fraction minus fraction numerator 1 over denominator square root of 3 left parenthesis 2 right parenthesis end root plus 1 end fraction end style over denominator straight h end fraction

                                  space space space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator square root of 7 plus 3 straight h end root end fraction end style minus begin display style fraction numerator 1 over denominator square root of 2 end fraction end style over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of 1 over straight h open square brackets fraction numerator square root of 7 minus square root of 7 plus 3 straight h end root over denominator square root of 7 space space square root of 7 plus 3 straight h end root end fraction close square brackets

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                      space space space space space space space space space space space space space space space space space space space space space space space space equals space limit as straight h rightwards arrow 0 of 1 fourth. fraction numerator 7 minus left parenthesis 7 plus 3 straight h right parenthesis over denominator square root of 7 square root of 7 plus 3 straight h end root left parenthesis square root of 7 plus square root of 7 plus 34 right parenthesis end root end fraction

                               space space space space space space space space space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator negative 3 over denominator square root of 7 plus square root of 7 plus 3 straight h end root left parenthesis square root of 7 plus square root of 7 plus 3 straight h right parenthesis end root end fraction equals fraction numerator negative 3 over denominator square root of 7 square root of 7 left parenthesis square root of 7 plus square root of 7 right parenthesis end fraction equals fraction numerator negative 3 over denominator 14 square root of 7 end fraction

                                




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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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    30.

    Find the derivative of f(x) = 

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