Khan Academy
Khan Academy: 2nd Order Linear Homogeneous Differential Equations 2
Let's find the general solution!
Khan Academy
Khan Academy: Analyzing Unbounded Limits: Mixed Function
Sal analyzes the behavior of f(x)=x/[1-cos(x-2)] around its asymptote at x=2. [6:16]
Khan Academy
Khan Academy: Analyzing Unbounded Limits: Rational Function
Sal analyzes the behavior of f(x)=-1/(x-1)^2 around its asymptote at x=1.
Khan Academy
Khan Academy: Analyzing Related Rates Problems: Equations (Trig)
Finding the rate of change of an angle that a falling ladder forms with the ground.
Khan Academy
Khan Academy: Analyzing Related Rates Problems: Expressions
When we have a related rates problem on our hands, it's best to first make sure we understand all the involved quantities.
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Khan Academy: Analyzing Related Rates Problems: Equations (Pythagoras)
A crucial part of solving related rates problems is picking an equation that correctly relates the quantities. We recommend making a diagram before doing that.
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Khan Academy: Analyzing a Function With Its Derivative
Taking the derivative of f(x)=x^3-12x+2 and graphing the derivative, so we can tell when f is increasing or decreasing, and where is its relative extremum points.
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Khan Academy: Analyzing Mistakes When Finding Extrema (Example 2)
Analyzing the work of someone who tried to find extrema of a function, to see whether they made mistakes.
Khan Academy
Khan Academy: Analyzing Mistakes When Finding Extrema (Example 1)
Analyzing the work of someone who tried to find extrema of a function, to see whether they made mistakes.
Khan Academy
Khan Academy: Absolute Minima & Maxima (Entire Domain)
Sal analyzes the absolute minimum and maximum points of g(x)=x^2ln(x) over its entire domain.
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Khan Academy: Analyzing Concavity (Algebraic)
Sal finds the intervals where g(x)=-x^4+6x^2-2x-3 is concave down/up by finding where its second derivative, g'', is positive/negative.
Khan Academy
Khan Academy: Alternating Series Test
When a series alternates (plus, minus, plus, minus,...) there's a fairly simple way to determine whether it converges or diverges: see if the terms of the series approach 0.
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Khan Academy: Alternating Series Remainder
By computing only the first few terms of an alternating series, we can get a pretty good estimate for the infinite sum. See why.
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Khan Academy: Analyzing Motion Problems: Total Distance Traveled
Finding the appropriate expression to use when looking for the total distance traveled over a certain time interval.
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Khan Academy: Analyzing Motion Problems: Position
Finding the appropriate expression to use when looking for the position at a certain time.
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Khan Academy: Analyzing Problems Involving Definite Integrals
See worked example of how to find the appropriate expression to use in order to solve word problems using definite integrals.
Khan Academy
Khan Academy: 2015 Ap Calculus Ab/bc 3 Cd
Accelerations and average velocity from velocity function.
