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
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) \((f \: g)' (1) = 0\)
Soal 03
Soal 04
Soal 05
Soal 06
Soal 07
Soal 08
Soal 09
Soal 10
Soal 11
Soal 12
Soal 13
Soal 14
Soal 15