Soal 01

SIMAK UI 2010 Matematika Dasar 203

${\displaystyle \underset{x\to \sim }{lim}{({\left({\displaystyle \frac{1}{2}}\right)}^{3x}+{\left({\displaystyle \frac{1}{2}}\right)}^x)}^{\frac{1}{x^2}}=\dots }$

(A)   −4

(B)   −2

(C)   1

(D)   2

(E)   3

 

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Soal 02

SIMAK UI 2019 Matematika Dasar 521

Jika $f$ dan $g$ adalah fungsi yang dapat diturunkan di $R$ sehingga

${\displaystyle \underset{h\to 0}{lim}{\displaystyle \frac{f(x+h)(g(x)-g(x+h))}{(k^2-1)h}}={\displaystyle \frac{x^2-1}{1+k}}}$, dan

${\displaystyle \underset{h\to 0}{lim}{\displaystyle \frac{g(x)(f(x)-f(x+h))}{(k^2-1)h}}={\displaystyle \frac{x^2-1}{1-k}}}$ untuk $k>1$,

maka ...

(1)   $(fg{)}^{\prime }(0)=2$

(2)   $(fg{)}^{\prime }(c)=2(x^2-1)$

(3)   $(fg{)}^{\prime }(0)=2(1-k^2)$

(4)   $(fg{)}^{\prime }(1)=0$

 

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Soal 03

 

 

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Soal 04

 

 

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Soal 05

 

 

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Soal 06

 

 

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Soal 07

 

 

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Soal 08

 

 

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Soal 09

 

 

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Soal 10

 

 

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Soal 11

 

 

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Soal 12

 

 

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Soal 13

 

 

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Soal 14

 

 

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Soal 15