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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.

Let f(x) = x²-2

Now, f (10) denote the derivative of x²-2 at x = 10.

∴ f' (10) $space space space space space space space space space space space space space space space space space space space space space space equals limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis 10 plus straight h right parenthesis minus straight f left parenthesis 10 right parenthesis over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator left square bracket 10 plus straight h right square bracket squared minus 2 right square bracket minus left parenthesis left parenthesis 10 right parenthesis squared minus 2 right square bracket over denominator straight h end fraction$

$space space space space space space space space space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator 100 plus straight h squared minus 20 straight h minus 2 minus 100 plus 2 over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator straight h squared plus 20 straight h over denominator straight h end fraction$

$space space space space space space space equals space space space limit as straight h rightwards arrow 0 of left parenthesis straight h plus 20 right parenthesis equals 0 plus 20$

Hence, f(10)=20