Soal 01

SIMAK UI 2010 Matematika Dasar 203

\(\displaystyle \lim_{x \rightarrow \sim} \left(\left(\dfrac 12 \right)^{3x} + \left(\dfrac 12 \right)^{x} \right)^{\frac {1}{x^2}} = \dotso\)

(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

\(\displaystyle \lim_{h \rightarrow 0} \dfrac {f(x + h) (g(x) - g(x + h))}{\left(k^2 - 1\right) h} = \dfrac {x^2 - 1}{1 + k}\), dan

\(\displaystyle \lim_{h \rightarrow 0} \dfrac {g(x) (f(x) - f(x + h))}{\left(k^2 - 1\right) h} = \dfrac {x^2 - 1}{1 - k}\) untuk \(k > 1\),

maka ...

(1)   \((f \: g)' (0)  = 2\)

(2)   \((f \: g)' (c)  = 2 \left(x^2 - 1 \right)\)

(3)   \((f \: g)' (0)  = 2 \left(1 - k^2 \right)\)

(4)   \((f \: g)' (1)  = 0\)

 

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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