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Mathematics for Economists
Chapter 5
Limits and continuity
Rough introduction to limits
Rough introduction to limits at infinity
Rough introduction to infinite limits
Rough introduction to continuity
Limit laws
Continuity laws
Limits and continuity: Problems
Problem: Calculate limits
Problem: Calculate limits
Problem: Calculate limit
Problem: Calculate limit by trying a small value
Problem: Calculate limit by trying a small value
Problem: Calculate limit
Problem: Determine if a function is continuous
Problem: Determine if a function is continuous
Problem: Determine if a function is continuous
Problem: Make a function continuous
Basic derivatives
Introduction to derivatives
Derivatives
Rules for differentiation
Derivatives and its relationship to increasing and decreasing functions
Basic derivatives: Problems
Problem: Find derivatives from the graph
Problem: Find the derivative using the definition
Problem: Find the derivative using the definition and the equation of the tangent
Problem: Find the slope of the tangent
Problem: Economic interpretation of slope and intercept
Problem: Find marginal profit, revenue and cost
Problem: Compute derivatives
Problem: Find the derivative of a composite function
Problem: Compute derivatives
Problem: Differentiate functions
Problem: Differentiate functions
Problem: Differentiate functions
Problem: Differentiate functions
Problem: Determine when a function is increasing/decreasing
Problem: Determine when a function is increasing
Problem: Economic interpretation of the derivative of an exponential function
Problem: Find the equation of the tangent
Chain rule
Chain rule
Problem: Differentiate using the chain rule
Problem: Differentiate function
Problem: Compute derivatives
Problem: Compute derivatives
Problem: Determine when a function is increasing
Problem: Find derivatives
Higher order derivatives
Higher order derivatives
Derivatives and its relationship to convex and concave functions
Problem: Compute second derivatives
Problem: Compute second derivative
Problem: Compute higher order derivatives
Problem: Find first and second order derivatives
Problem: Find first and second order derivatives
Implicit differentiation and the derivative of the inverse
Implicit differentiation
Inverse function theorem
Derivative of the inverse of a function
Implicit differentiation and the derivative of the inverse: Problems
Problem: Implicit differentiation
Problem: Implicit differentiation, first and second order
Problem: Implicit differentiation of indifference curve
Problem: Derivative of the inverse function
Problem: Derivative of the inverse function
Problem: Derivative of the inverse function
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Chapter 5
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Problem: Determine when a function is increasing/decreasing
Problem
Examine where
f
(
x
)
=
x
2
−
4
x
+
3
is increasing/decr
easing
Show solution
Solution
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