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# ← Calculus: Ch. 1Test

### Question Limit

of 44 available terms

### 5 Matching Questions

1. Theorem of tangent of two line
2. Cotangent function
3. The real line
4. Slope of line l with points (x_1, y_1) and (x_2, y_2)
5. Slope-intercept equation
1. a (-∞, ∞) <-> all real numbers
2. b Let l_1 and l_2 be two nonvertical lines that are not perpendicular, with slopes m_1 and m_2 respectively. The tangent of the angle θ from l_1 to l_2 is given by tan θ = (m_2 - m_1) / (1 + (m_1)(m_2))
3. c cot x = cos x / sin x for x /= nπ, n any integer
4. d m = (y_2 - y_1) / (x_2 - x_1)
5. e y = mx + b

### 5 Multiple Choice Questions

1. Replace f (x) by f (x) - c
2. Let a and b be fixed positive numbers. For any numbers x and y we have
(1) a^(x + y) = (a^x)(a^y)
(2) a^xy = (a^x)^y = (a^y)^x
(3) (ab)^x = (a^x)(b^x)
(4) a^1 = a
(5) a^-1 = 1/(a^x) = (1/a)^x
(6) (a/b)^x = (a^x)/(b^x)
(7) a^0 = 1
3. Replace f (x) by f (x + c)
4. If a < b and b < c, then a < c.
5. Let l_1 and l_2 be nonvertical lines with sloped m_1 and m_2. Then l_1 and l_2 are parallel if and only if m_1 = m_2.

### 5 True/False Questions

1. How to solve an inequality1) Algebraically make one side equal to zero.
2) Express the other side as a product.
3) Find the zeroes of factors of the product.
4) Draw a diagram that shows the signs of the factors of the product from -∞ to ∞.
5) Deduce the values of x for which the product satisfies the inequality.

2. 6 laws of logarithmsLet a and b be fixed positive numbers. For any numbers x and y we have
(1) a^(x + y) = (a^x)(a^y)
(2) a^xy = (a^x)^y = (a^y)^x
(3) (ab)^x = (a^x)(b^x)
(4) a^1 = a
(5) a^-1 = 1/(a^x) = (1/a)^x
(6) (a/b)^x = (a^x)/(b^x)
(7) a^0 = 1

3. Function, domain, ruleOne of these three:
[a, b] <-> all x such that a <= x <= b
[a, ∞) <-> all x such that a <= x
(-∞, a] <-> all x such that x <= a

4. Arc length in terms of radiansOne of these three:
[a, b] <-> all x such that a <= x <= b
[a, ∞) <-> all x such that a <= x
(-∞, a] <-> all x such that x <= a

5. Open intervalOne of these three:
(a, b) <-> all x such that a < x < b
(a, ∞) <-> all x such that a < x
(-∞, a) <-> all x such that x < a