Soal 01
\(\displaystyle \lim_{x \rightarrow 0} \: \frac {1}{x} = \dotso\)
(A) \(0\)
(B) \(\sim\)
(C) \(− \sim\)
(D) \(+ \sim\)
(E) Tidak ada
Soal 02
Jika \(\displaystyle \lim_{x \rightarrow p} \: f(x) = a\) dan \(\displaystyle \lim_{x \rightarrow p} \: g(x) = b\), nilai dari \(\displaystyle \lim_{x \rightarrow p} \: (f(x) + g(x))^2 = \dotso\)
(A) \(a + b\)
(B) \(a + b + ab\)
(C) \(a^2 + b^2\)
(D) \(a^2 + b^2 + ab\)
(E) \(a^2 + b^2 + 2ab\)
Soal 03
\(\displaystyle \lim_{x \rightarrow 1} \: \frac {x^2 + 3}{x + 1} = \dotso\)
(A) \(0\)
(B) \(1\)
(C) \(2\)
(D) \(3\)
(E) \(4\)
Soal 04
\(\displaystyle \lim_{x \rightarrow 2} \: \frac {3x - 6}{x - 2} = \dotso\)
(A) \(0\)
(B) \(1\)
(C) \(2\)
(D) \(3\)
(E) \(4\)
Soal 05
\(\displaystyle \lim_{x \rightarrow 3} \: \frac {x^3 - 27}{x^2 - 9} = \dotso\)
(A) \(1,5\)
(B) \(3,0\)
(C) \(4,5\)
(D) \(6,0\)
(E) \(9,0\)
Soal 06
\(\displaystyle \lim_{x \rightarrow 5} \: \frac {x^2 - 9x + 20}{x - 5} = \dotso\)
(A) \(1\)
(B) \(2\)
(C) \(3\)
(D) \(4\)
(E) \(5\)
Soal 07
\(\displaystyle \lim_{x \rightarrow 0} \: \frac {x^3 - 3x^2 + 2x}{x^2 - 3x} = \dotso\)
(A) \(- \frac 32\)
(B) \(- \frac 23\)
(C) \(1\)
(D) \(\frac 23\)
(E) \(\frac 32\)
Soal 08
\(\displaystyle \lim_{x \rightarrow 0} \: \frac {\sqrt{x} - x}{\sqrt{x} + x} = \dotso\)
(A) \(−1\)
(B) \(0\)
(C) \(0,5\)
(D) \(1\)
(E) \(\sim\)
Soal 09
\(\displaystyle \lim_{x \rightarrow 2} \: \frac {2x^3 + x^2 - 7x - 6}{x^2 - 2x} = \dotso\)
(A) \(7,5\)
(B) \(9,0\)
(C) \(10,5\)
(D) \(11\)
(E) \(13,5\)
Soal 10
\(\displaystyle \lim_{x \rightarrow 1} \: \left( \frac {2}{x^2 - 1} - \frac {1}{x - 1} \right) = \dotso\)
(A) \(- 1\)
(B) \(- \frac 12\)
(C) \(0\)
(D) \(\frac 12\)
(E) \(1\)
Soal 11
\(\displaystyle \lim_{x \rightarrow 0} \: \frac {\sqrt{2 + x} - \sqrt{2 - x}}{x} = \dotso\)
(A) \(\frac 12 \sqrt{2}\)
(B) \(\sqrt{2}\)
(C) \(2\sqrt{2}\)
(D) \(1\)
(E) \(0\)
Soal 12
\(\displaystyle \lim_{x \rightarrow 2} \: \frac {x - 2}{\sqrt{2x^2 + 1} - 3} = \dotso\)
(A) \(\frac 14\)
(B) \(\frac 24\)
(C) \(\frac 34\)
(D) \(1\)
(E) \(\frac 54\)
Soal 13
\(\displaystyle \lim_{x \rightarrow 1} \: \frac {x^n - 1}{x - 1} = \dotso\)
(A) \(-1\)
(B) \(0\)
(C) \(1\)
(D) \(n\)
(E) \(-n\)
Soal 14
Jika \(\displaystyle \lim_{x \rightarrow a} \: \frac {x^2 + ax + b}{x - a} = 9\), maka nilai dari \(a - b = \dotso\)
(A) \(-18\)
(B) \(-9\)
(C) \(9\)
(D) \(18\)
(E) \(21\)
Soal 15
DIketahui fungsi di bawah ini:
\(f(x)=\begin{cases} x + 6 & , \: x \leq 3 \\\\ x^2 & , \: x > 0\end{cases}\)
Pernyataan yang tepat di bawah ini:
(1) \(f(3) = 9\)
(2) \(\displaystyle \lim_{x \rightarrow 3^-} \: f(x) = 9\)
(3) \(\displaystyle \lim_{x \rightarrow 3^+} \: f(x) = 9\)
(4) fungsi kontinu pada x = 3
Anda bisa menjawab lebih dari satu pilihan.
Soal 16
\(\displaystyle \lim_{x \rightarrow \sim} \: \frac {1 + 2x^2 - 6x^3}{-3x^3 + 5x^2 + 8} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(2\)
(E) \(\sim\)
Soal 17
\(\displaystyle \lim_{x \rightarrow \sim} \: \frac {5x - 8x^4}{9x^3 + 4} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(2\)
(E) \(\sim\)
Soal 18
\(\displaystyle \lim_{x \rightarrow \sim} \: \frac {2x^3 - 4x}{1 - 5x - 5x^6} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(2\)
(E) \(\sim\)
Soal 19
\(\displaystyle \lim_{x \rightarrow \sim} \: \frac {\sqrt{x^2 + 1} + \sqrt{16x^2 + 4}}{\sqrt{9x^2 + 2} + \sqrt{4x^2 - 1}} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(1\)
(E) \(2\)
Soal 20
\(\displaystyle \lim_{x \rightarrow \sim} \: \frac {3 - 5x + \sqrt{16x^2 - 9}}{6x + 4 - \sqrt{25x^2 + 7}} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(1\)
(E) \(2\)
Soal 21
\(\displaystyle \lim_{x \rightarrow \sim} \: \sqrt{x + 5} - \sqrt{x - 2} = \dotso \)
(A) \(0\)
(B) \(3\)
(C) \(7\)
(D) \(10\)
(E) \(\sim\)
Soal 22
\(\displaystyle \lim_{x \rightarrow \sim} \: \sqrt{8x + 3} - \sqrt{6x - 1} = \dotso \)
(A) \(0\)
(B) \(1\)
(C) \(2\)
(D) \(3\)
(E) \(\sim\)
Soal 23
\(\displaystyle \lim_{x \rightarrow \sim} \: \sqrt{x^2 + 5x - 8} - \sqrt{x^2 - x + 6} = \dotso \)
(A) \(3\)
(B) \(4\)
(C) \(5\)
(D) \(6\)
(E) \(7\)
Soal 24
\(\displaystyle \lim_{x \rightarrow \sim} \: x + 4 - \sqrt{x^2 + 6x - 3} = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(1\)
(E) \(2\)
Soal 25
\(\displaystyle \lim_{x \rightarrow \sim} \: \sqrt{9x^2 - 24x + 1} - 3x + 2 = \dotso \)
(A) \(-2\)
(B) \(-1\)
(C) \(0\)
(D) \(1\)
(E) \(2\)