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Pertanyaan

limit as x rightwards arrow 1 of x squared minus 4 x equals...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of x squared minus 4 x end cell equals cell open parentheses 1 close parentheses squared minus 4 open parentheses 1 close parentheses end cell row blank equals cell 1 minus 4 end cell row blank equals cell negative 3 end cell end table

Jadi, nilai dari limit as x rightwards arrow 1 of x squared minus 4 x equals negative 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

=...

Pembahasan Soal:

Dengan mensubtitusi nilai x ke dalam fungsi, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of open parentheses x squared plus 2 x minus 2 close parentheses end cell equals cell open parentheses negative 2 close parentheses squared plus 2 left parenthesis negative 2 right parenthesis minus 2 end cell row blank equals cell 4 minus 4 minus 2 end cell row blank equals cell negative 2 end cell end table

Maka, limit as x rightwards arrow negative 2 of open parentheses x squared plus 2 x minus 2 close parentheses equals negative 2

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Roboguru

Pembahasan Soal:

Menentukan limit fungsi dengan metode subtitusi, jika ada left parenthesis straight a minus straight b right parenthesis squared equals straight a to the power of 2 end exponent minus 2 ab plus straight b squared maka dijabarkan dahulu open parentheses x minus 3 close parentheses squared.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator open parentheses x minus 3 close parentheses squared minus 9 over denominator x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator x squared minus 6 x plus 9 minus 9 over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared minus 6 x over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x cross times left parenthesis x minus 6 right parenthesis over denominator up diagonal strike x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of x minus 6 end cell row blank equals cell 0 minus 6 end cell row blank equals cell negative 6 end cell end table

Jadi, limit as x rightwards arrow 0 of fraction numerator open parentheses x minus 3 close parentheses squared minus 9 over denominator x end fraction adalah negative 6.

0

Roboguru

Nilai dari  =

Pembahasan Soal:

begin mathsize 14px style x equals 5 end style disubtitusikan pada limit tersebut

   begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of space x squared minus 2 x minus 10 end cell equals cell 5 squared minus 2 open parentheses 5 close parentheses minus 10 end cell row cell space space end cell equals cell 25 minus 10 minus 10 end cell row blank equals 5 end table end style  

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 5 of space x squared minus 2 x minus 10 end style adalah 5  

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Roboguru

Nilai

Pembahasan Soal:

Dengan metode substitusi, diperoleh nilai limit tersebut adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 2 x over denominator x plus 2 end fraction end cell equals cell fraction numerator 2 open parentheses 0 close parentheses over denominator 0 plus 2 end fraction end cell row blank equals cell 0 over 2 end cell row blank equals 0 end table end style

Jadi, jawabannya adalah 0.

0

Roboguru

Tentukan dari fungsi .

Pembahasan Soal:

Diketahui fungsi f open parentheses x close parentheses equals x squared plus 2, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus h close parentheses end cell equals cell open parentheses x plus h close parentheses squared plus 2 end cell row blank equals cell x squared plus 2 x h plus h squared plus 2 end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses x squared plus 2 x h plus h squared plus 2 close parentheses minus open parentheses x squared plus 2 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x h plus h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator h open parentheses 2 x plus h close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 2 x plus h end cell row blank equals cell 2 x end cell end table

Jadi, limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction dari fungsi f open parentheses x close parentheses equals x squared plus 2 adalah 2 x.

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