Question

1) Plot the function over the given interval: $f(x) = \frac{3|x| - 1}{10x^2 + 1}$, $-1 \leq x \leq 2$ 2) Evaluate the limit: $\lim_{x \to 0} \frac{\sin(3x) - 3x + \frac{x^3}{2} - \frac{91x^5}{90}}{x^3}$ 3) Solve following linear system and find $\sum_{i=1}^{102} x_i^2$ $\begin{cases} x_1 + 4x_2 = 1\\x_i + 4x_{i+1} + x_{i+2} = i, \quad i = 1, 2, \dots, 100\\x_{101} + 5x_{102} = 100 \end{cases}$ 4) The function Q has 14 roots on the intervals (0,1), find these roots. $Q(x) = \frac{358}{5} - \frac{580384}{5}x - \frac{11501028}{5}x^2 - \frac{172256000}{5}x^3 - \frac{416117625}{5}x^4 \\ + \frac{1180038528}{5}x^5 + \frac{1760122364}{5}x^6 + \frac{11778624}{5}x^7 \\ + \ln(x) \left( -7 - 18816x - 2857680x^2 - 70560000x^3 \\ - 400207500x^4 - 553246848x^5 - 144288144x^6 \right)$

          1) Plot the function over the given interval:
$f(x) = \frac{3|x| - 1}{10x^2 + 1}$, $-1 \leq x \leq 2$

2) Evaluate the limit:
$\lim_{x \to 0} \frac{\sin(3x) - 3x + \frac{x^3}{2} - \frac{91x^5}{90}}{x^3}$

3) Solve following linear system and find $\sum_{i=1}^{102} x_i^2$
$\begin{cases} x_1 + 4x_2 = 1\\x_i + 4x_{i+1} + x_{i+2} = i, \quad i = 1, 2, \dots, 100\\x_{101} + 5x_{102} = 100 \end{cases}$

4) The function Q has 14 roots on the intervals (0,1), find these roots.
$Q(x) = \frac{358}{5} - \frac{580384}{5}x - \frac{11501028}{5}x^2 - \frac{172256000}{5}x^3 - \frac{416117625}{5}x^4 \\
+ \frac{1180038528}{5}x^5 + \frac{1760122364}{5}x^6 + \frac{11778624}{5}x^7 \\
+ \ln(x) \left( -7 - 18816x - 2857680x^2 - 70560000x^3 \\
- 400207500x^4 - 553246848x^5 - 144288144x^6 \right)$

1) Plot the function over the given interval:
f(x) = (3|x| - 1)/(10x^2 + 1), -1 ≤ x ≤ 2

2) Evaluate the limit:
limx → 0(sin(3x) - 3x + (x^3)/(2) - (91x^5)/(90))/(x^3)

3) Solve following linear system and find ∑i=1^102 xi^2
x1 + 4x2 = 1
xi + 4xi+1 + xi+2 = i, i = 1, 2, …, 100
x101 + 5x102 = 100

4) The function Q has 14 roots on the intervals (0,1), find these roots.
Q(x) = (358)/(5) - (580384)/(5)x - (11501028)/(5)x^2 - (172256000)/(5)x^3 - (416117625)/(5)x^4

+ (1180038528)/(5)x^5 + (1760122364)/(5)x^6 + (11778624)/(5)x^7

+ ln(x) ( -7 - 18816x - 2857680x^2 - 70560000x^3

- 400207500x^4 - 553246848x^5 - 144288144x^6 )

Added by Glenda V.

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