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48) Fundamental Theorem of Calculus
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Classroom Contents
Learn Calculus 1 in One Video
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- 1 2) Computing Limits from a Graph
- 2 3) Computing Basic Limits by plugging in numbers and factoring
- 3 4) Limit using the Difference of Cubes Formula 1
- 4 5) Limit with Absolute Value
- 5 6) Limit by Rationalizing
- 6 7) Limit of a Piecewise Function
- 7 8) Trig Function Limit Example 1
- 8 9) Trig Function Limit Example 2
- 9 10) Trig Function Limit Example 3
- 10 11) Continuity
- 11 12) Removable and Nonremovable Discontinuities
- 12 13) Intermediate Value Theorem
- 13 14) Infinite Limits
- 14 15) Vertical Asymptotes
- 15 16) Derivative (Full Derivation and Explanation)
- 16 17) Definition of the Derivative Example
- 17 18) Derivative Formulas
- 18 19) More Derivative Formulas
- 19 20) Product Rule
- 20 21) Quotient Rule
- 21 22) Chain Rule
- 22 23) Average and Instantaneous Rate of Change (Full Derivation)
- 23 24) Average and Instantaneous Rate of Change (Example)
- 24 25) Position, Velocity, Acceleration, and Speed (Full Derivation)
- 25 26) Position, Velocity, Acceleration, and Speed (Example)
- 26 27) Implicit versus Explicit Differentiation
- 27 28) Related Rates
- 28 29) Critical Numbers
- 29 30) Extreme Value Theorem
- 30 31) Rolle's Theorem
- 31 32) The Mean Value Theorem
- 32 33) Increasing and Decreasing Functions using the First Derivative
- 33 34) The First Derivative Test
- 34 35) Concavity, Inflection Points, and the Second Derivative
- 35 36) The Second Derivative Test for Relative Extrema
- 36 37) Limits at Infinity
- 37 38) Newton's Method
- 38 39) Differentials: Deltay and dy
- 39 40) Indefinite Integration (theory)
- 40 41) Indefinite Integration (formulas)
- 41 41) Integral Example
- 42 42) Integral with u substitution Example 1
- 43 43) Integral with u substitution Example 2
- 44 44) Integral with u substitution Example 3
- 45 45) Summation Formulas
- 46 46) Definite Integral (Complete Construction via Riemann Sums)
- 47 47) Definite Integral using Limit Definition Example
- 48 48) Fundamental Theorem of Calculus
- 49 49) Definite Integral with u substitution
- 50 50) Mean Value Theorem for Integrals and Average Value of a Function
- 51 51) Extended Fundamental Theorem of Calculus (Better than 2nd FTC)
- 52 error here: forgot to cube the (3/2) here at the end, otherwise ok!
- 53 53) The Natural Logarithm ln(x) Definition and Derivative
- 54 54) Integral formulas for 1/x, tan(x), cot(x), csc(x), sec(x), csc(x)
- 55 55) Derivative of e^x and it's Proof
- 56 56) Derivatives and Integrals for Bases other than e
- 57 57) Integration Example 1
- 58 58) Integration Example 2
- 59 59) Derivative Example 1
- 60 60) Derivative Example 2
