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Hitunglah setiap limit fungsi berikut. a. x→2lim​f(x), untuk f(x)={3−2xx2−5​x≤2x>2​   b. x→1lim​g(x), untuk g(x)={x−1x2−x​1−x​​x<1x≥1​

Pertanyaan

Hitunglah setiap limit fungsi berikut.

a. limit as x rightwards arrow 2 of f left parenthesis x right parenthesis comma space untuk space f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 3 minus 2 x end cell cell x less or equal than 2 end cell row cell x squared minus 5 end cell cell x greater than 2 end cell end table close  

b. limit as x rightwards arrow 1 of g left parenthesis x right parenthesis comma space untuk space g left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell fraction numerator x squared minus x over denominator x minus 1 end fraction end cell cell x less than 1 end cell row cell square root of 1 minus x end root end cell cell x greater or equal than 1 end cell end table close  

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

 nilailimit as x rightwards arrow 1 of g open parentheses x close parentheses tidak ada.

Pembahasan

a. limit as x rightwards arrow 2 of f left parenthesis x right parenthesis comma space untuk space f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 3 minus 2 x end cell cell x less or equal than 2 end cell row cell x squared minus 5 end cell cell x greater than 2 end cell end table close

Fungsi f open parentheses x close parentheses terbagi menjadi dua interval, maka untuk menentukan limit as x rightwards arrow 2 of space f open parentheses x close parentheses, harus menentukan dulu limit kanan dan kiri sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 to the power of minus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 2 to the power of minus of open parentheses 3 minus 2 x close parentheses end cell row blank equals cell 3 minus 2 left parenthesis 2 right parenthesis end cell row blank equals cell 3 minus 4 end cell row blank equals cell negative 1 end cell end table
 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 to the power of plus of f open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 2 to the power of plus of open parentheses x squared minus 5 close parentheses end cell row blank equals cell 2 squared minus 5 end cell row blank equals cell 4 minus 5 end cell row blank equals cell negative 1 end cell end table  

Berdasarkan uraian di atas, limit as x rightwards arrow 2 to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow 2 to the power of plus of f open parentheses x close parentheses equals negative 1, maka limit as x rightwards arrow 2 of f open parentheses x close parentheses equals negative 1.

Dengan demikian, limit as x rightwards arrow 2 of f open parentheses x close parentheses equals negative 1.

b. limit as x rightwards arrow 1 of g left parenthesis x right parenthesis comma space untuk space g left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell fraction numerator x squared minus x over denominator x minus 1 end fraction end cell cell x less than 1 end cell row cell square root of 1 minus x end root end cell cell x greater or equal than 1 end cell end table close

Fungsi g open parentheses x close parentheses terbagi menjadi dua interval, maka untuk menentukan limit as x rightwards arrow 1 of space g open parentheses x close parentheses, harus menentukan dulu limit kanan dan kiri sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 to the power of minus of g open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 1 to the power of minus of open parentheses fraction numerator x squared minus x over denominator x minus 1 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 to the power of minus of fraction numerator x up diagonal strike left parenthesis x minus 1 right parenthesis end strike over denominator open parentheses up diagonal strike x minus 1 end strike close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 to the power of minus of x end cell row blank equals 1 end table
 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 to the power of plus of g open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 1 to the power of plus of square root of 1 minus x end root end cell row blank equals cell square root of 1 minus 1 end root end cell row blank equals cell square root of 0 end cell row blank equals 0 end table   

 

Berdasarkan uraian di atas, limit as x rightwards arrow 1 to the power of minus of g open parentheses x close parentheses not equal to limit as x rightwards arrow 1 to the power of plus of g open parentheses x close parentheses, maka nilailimit as x rightwards arrow 1 of g open parentheses x close parentheses tidak ada.

Dengan demikian, nilailimit as x rightwards arrow 1 of g open parentheses x close parentheses tidak ada.

49

5.0 (1 rating)

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