Checkpoint 5.55. QuickCheck 1.
The value of \(e^2\) is closest to
- \(\displaystyle 3\)
- \(\displaystyle 5\)
- \(\displaystyle 7\)
- \(\displaystyle 9\)
Answer.
\(\text{Choice 3}\)
Solution.
7
\(x\) | \(y=2^x\) | \(y=e^x\) | \(y=3^x\) |
\(-3\) | \(0.125\) | \(0.050\) | \(0.037\) |
\(-2\) | \(0.250\) | \(0.135\) | \(0.111\) |
\(-1\) | \(0.500\) | \(0.368\) | \(0.333\) |
\(0\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(2\) | \(2.718\) | \(3\) |
\(2\) | \(4\) | \(7.389\) | \(9\) |
\(3\) | \(8\) | \(20.086\) | \(27\) |
\(x\) | \(y=\ln x\) |
\(0.050\) | \(-3\) |
\(0.135\) | \(-2\) |
\(0.368\) | \(-1\) |
\(1\) | \(0\) |
\(2.718\) | \(1\) |
\(7.389\) | \(2\) |
\(20.086\) | \(3\) |
\(t\) | \(0\) | \(10\) | \(20\) | \(30\) |
\(N(t)\) |
\(t\) | \(40\) | \(50\) | \(60\) |
\(N(t)\) |
\(t\) | \(0\) | \(10\) | \(20\) | \(30\) | \(40\) | \(50\) | \(60\) |
\(N(t)\) | \(25\) | \(12.41\) | \(6.16\) | \(3.06\) | \(1.52\) | \(0.75\) | \(0.37\) |
\(t\) | \(A(t)\) |
\(0\) | \(500\) |
\(1\) | \(541.64\) |
\(2\) | \(586.76\) |
\(3\) | \(635.62\) |
\(4\) | \(688.56\) |
\(5\) | \(745.91\) |
\(x\) | \(-10\) | \(-5\) | \(0\) | \(5\) | \(10\) | \(15\) | \(20\) |
\(f(x)\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) | \(\hphantom{0000}\) |
\(x\) | \(0\) | \(0.5\) | \(1\) | \(1.5\) | \(2\) | \(2.5\) |
\(e^x\) | \(\phantom{000} \) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) |
\(x\) | \(0\) | \(2\) | \(4\) | \(6\) | \(8\) | \(10\) |
\(e^x\) | \(\phantom{000} \) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) |
\(x\) | \(0\) | \(0.6931\) | \(1.3863\) | \(2.0794\) | \(2.7726\) | \(3.4657\) | \(4.1589\) |
\(e^x\) | \(\phantom{000} \) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) |
\(x\) | \(0\) | \(1.0986\) | \(2.1972\) | \(3.2958\) | \(4.3944\) | \(5.4931\) | \(6.5917\) |
\(e^x\) | \(\phantom{000} \) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) | \(\phantom{000}\) |
\(n\) | \(0.39\) | \(3.9\) | \(39\) | \(390\) |
\(\ln n\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(n\) | \(0.64\) | \(6.4\) | \(64\) | \(640\) |
\(\ln n\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(n\) | \(2\) | \(4\) | \(8\) | \(16\) |
\(\ln n\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
\(n\) | \(5\) | \(25\) | \(125\) | \(625\) |
\(\ln n\) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) | \(\hphantom{0000} \) |
Time (min) | \(0\) | \(10\) | \(20\) | \(30\) | \(40\) | \(50\) | \(60\) | \(70\) | \(80\) | \(90\) |
Counts/sec | \(120\) | \(90\) | \(69\) | \(54\) | \(42\) | \(33\) | \(25\) | \(19\) | \(15\) | \(13\) |
Time (min) | \(0\) | \(10\) | \(20\) | \(30\) | \(40\) | \(50\) | \(60\) | \(70\) | \(80\) | \(90\) |
Counts/sec | \(180\) | \(112\) | \(71\) | \(45\) | \(28\) | \(18\) | \(11\) | \(7\) | \(4\) | \(3\) |