Roboguru

= ...

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator sin squared x minus cos space x plus 1 over denominator x space tan space x end fraction end style = ...

  1. begin mathsize 14px style 3 over 2 end style

  2. begin mathsize 14px style 1 half end style

  3. begin mathsize 14px style negative 1 half end style

  4. -1

  5. -2

Jawaban:

Ingat!

cos x = 1 - 2 sin2 begin mathsize 14px style 1 half end stylex

maka:

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator sin squared x minus cos space x plus 1 over denominator x space tan space x end fraction end style = begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator sin squared space x minus open parentheses 1 minus 2 sin squared space 1 half x close parentheses plus 1 over denominator x space tan space x end fraction end style

                                    = begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator sin squared space x minus 1 plus 2 sin squared space 1 half x plus 1 over denominator x space tan space x end fraction end style

                                    = begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator sin squared space x plus 2 sin squared space 1 half x over denominator x space tan space x end fraction end style

                                    = begin mathsize 14px style limit as x rightwards arrow 0 of open parentheses fraction numerator horizontal strike sin space x end strike. horizontal strike sin space x end strike over denominator horizontal strike x horizontal strike space tan space x end strike end fraction plus fraction numerator 2 space horizontal strike sin 1 half horizontal strike x horizontal strike. sin end strike 1 half horizontal strike x over denominator horizontal strike x space horizontal strike tan space x end strike end fraction close parentheses end style

                                    = begin mathsize 14px style limit as x rightwards arrow 0 of open parentheses 1 plus 2.1 half.1 half close parentheses end style

                                    = begin mathsize 14px style 1 plus 1 half end style

                                    = begin mathsize 14px style 3 over 2 end style

0

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