MATH 110 Introduction to Statistics | Portage Learning | Academic Year 2026/2027 |
Comprehensive Examination — Modules 1–10 | 50 Verified Questions and Correct
Answer Rationales
1. Limits as x approaches +- infinity - ANSWERS-When you are taking limits as x approaches
+- infinity, you want to look at the highest power on top and bottom
2. CASE 1: The powers are the same - ANSWERS-Rule: divide coefficients
3. CASE 2: The power on bottom is bigger - ANSWERS-Rule: ZERO
4. CASE 3: The power on top is bigger - ANSWERS-Rule: DNE ( +- infinity)
5. Continuity - ANSWERS-A function is continuous at a point, a, if it satisfies the following:
1. F(a) exists
2. Lim x>a f(a) exists
3. The limit = f(a)
6. To make a piece wise function continuous: - ANSWERS-set lim x>a f(x) = f(a)
7. To find discontinuities of a rational function (fraction): - ANSWERS-find all values where
the denominator equals 0
8. What is a derivative? - ANSWERS-an instantaneous rate of change
Slope of the tangent line
Marginal
Dy/dx
9. Chain Rule
Derivative of (f(g(x)) - ANSWERS-f'(g(x)) * g'(x)
10. Product Rule
D/dx [f(x)g(x)] - ANSWERS-f(x)g'(x) + f'(x)g(x)
11. Quotient Rule
D/dx [f(x)/g(x)] - ANSWERS-g(x)f'(x) - f(x)g'(x) / (g(x))^2
12. To find the *slope of the tangent line* - ANSWERS-1. Take the derivative
2. Plug in the x value (before you simplify)
13. To fin the *equation of the a tangent line* - ANSWERS-1. Find a point on the line (x1, y1)
2. Find the slope of the tangent line (m)
4. Plug into point slope form: *y -y1 = m(x - x1)*
14. Rules of Differentiability - ANSWERS-1. If f(x) is differentiable at x=a, then it must be
continuous at x=a
2. If f(x) is not continuous at x=a, then it is not differentiable at x=a
Comprehensive Examination — Modules 1–10 | 50 Verified Questions and Correct
Answer Rationales
1. Limits as x approaches +- infinity - ANSWERS-When you are taking limits as x approaches
+- infinity, you want to look at the highest power on top and bottom
2. CASE 1: The powers are the same - ANSWERS-Rule: divide coefficients
3. CASE 2: The power on bottom is bigger - ANSWERS-Rule: ZERO
4. CASE 3: The power on top is bigger - ANSWERS-Rule: DNE ( +- infinity)
5. Continuity - ANSWERS-A function is continuous at a point, a, if it satisfies the following:
1. F(a) exists
2. Lim x>a f(a) exists
3. The limit = f(a)
6. To make a piece wise function continuous: - ANSWERS-set lim x>a f(x) = f(a)
7. To find discontinuities of a rational function (fraction): - ANSWERS-find all values where
the denominator equals 0
8. What is a derivative? - ANSWERS-an instantaneous rate of change
Slope of the tangent line
Marginal
Dy/dx
9. Chain Rule
Derivative of (f(g(x)) - ANSWERS-f'(g(x)) * g'(x)
10. Product Rule
D/dx [f(x)g(x)] - ANSWERS-f(x)g'(x) + f'(x)g(x)
11. Quotient Rule
D/dx [f(x)/g(x)] - ANSWERS-g(x)f'(x) - f(x)g'(x) / (g(x))^2
12. To find the *slope of the tangent line* - ANSWERS-1. Take the derivative
2. Plug in the x value (before you simplify)
13. To fin the *equation of the a tangent line* - ANSWERS-1. Find a point on the line (x1, y1)
2. Find the slope of the tangent line (m)
4. Plug into point slope form: *y -y1 = m(x - x1)*
14. Rules of Differentiability - ANSWERS-1. If f(x) is differentiable at x=a, then it must be
continuous at x=a
2. If f(x) is not continuous at x=a, then it is not differentiable at x=a
