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Calculus 1
Getting started
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Idea of the limit
introduction to limits and continuity (8:41)
Formal definition of the limit
one-sided limits (9:25)
proving that the limit does not exist (5:38)
precise definition of the limit (11:27)
precise definition of the limit, finding delta (6:14)
Combinations and composites
limits of combinations (8:55)
Continuity
introduction to continuity (3:31)
removable discontinuities (8:15)
Intermediate value theorem
intermediate value theorem overview (7:09)
intermediate value theorem with an interval (4:19)
intermediate value theorem without an interval (6:22)
Solving limits
solving limits with substitution (2:46)
solving limits with factoring (4:31)
solving limits with conjugate method (6:27)
infinite limits (vertical asymptotes) (7:02)
limits at infinity (horizontal asymptotes) (9:24)
crazy graphs (7:47)
trigonometric limits (4:49)
making the function continuous (11:10)
Squeeze theorem
squeeze theorem (4:35)
squeeze theorem, limit of an inequality (3:01)
Definition of the derivative
introduction to derivatives (7:48)
difference quotient (3:44)
definition of the derivative (12:14)
Derivative rules
power rule (10:13)
product rule, two functions (9:50)
product rule, three or more functions (7:06)
quotient rule (11:58)
reciprocal rule (8:12)
Chain rule
chain rule with power rule (6:26)
chain rule with product rule (8:35)
chain rule with quotient rule (7:15)
chain rule with trig functions (5:04)
Derivatives of trig functions
trigonometric derivatives (24:30)
inverse trigonometric derivatives (8:58)
hyperbolic derivatives (4:20)
inverse hyperbolic derivatives (4:40)
Derivatives of ln(x) and e^x
exponential derivatives (6:47)
logarithmic derivatives (11:50)
logarithmic differentiation (14:51)
derivative of x^x (6:14)
Tangent and normal lines
tangent lines (7:59)
value that makes two tangent lines parallel (15:18)
values that make the function differentiable (8:28)
horizontal and vertical tangent lines and differentiability (14:21)
normal lines (4:27)
average rate of change (5:52)
Implicit differentiation
implicit differentiation (10:23)
implicit differentiation, equation of the tangent line (19:32)
implicit differentiation, second derivatives (8:14)
Optimization
introduction to optimization (9:17)
critical points (16:04)
increasing and decreasing (8:15)
first derivative test (15:26)
concavity (7:06)
second derivative test (3:42)
Sketching graphs
vertical asymptotes (9:56)
horizontal asymptotes (8:11)
slant asymptotes (3:55)
sketching graphs (9:57)
extrema on a closed interval (13:18)
sketching f(x) given the graph of f'(x), or vice versa (29:44)
Linear approximation and linearization
linear approximation (4:22)
linear approximation to estimate a root (8:09)
linearization (3:53)
Related rates
related rates (45:44)
Applied optimization
introduction to applied optimization
dimensions of a rectangle that maximize its area (6:06)
dimensions of a rectangle that minimize its perimeter (10:24)
dimensions that minimize page size with a given printed area (14:00)
two real numbers with minimum product (6:51)
two real numbers with minimum sum of squares (8:42)
point on the line closest to another point (7:17)
time when velocity is minimum (5:43)
dimensions that maximize the volume of a box (10:08)
dimensions that minimize the surface area of an open top box (11:35)
width that minimizes the surface area of an open top box (11:30)
dimensions that maximize the volume of a cylinder (12:32)
dimensions that minimize the surface area of a cylinder (8:37)
maximum volume of a cone shaped cup (11:03)
production level and sale price that maximize profit (10:21)
sales level that maximizes revenue (7:35)
maximum area of a rectangle inscribed in a semicircle (15:46)
dimensions that maximize the area of a rectangle inscribed in a triangle (13:16)
maximum volume of a cylinder inscribed in a sphere (14:03)
applied optimization quiz
Derivative theorems
mean value theorem (11:20)
rolle's theorem (5:11)
newton's method (9:21)
l'hospital's rule (3:15)
Physics
position function (3:51)
position function of a particle (19:56)
vertical motion, ball thrown up from the ground (9:36)
vertical motion, coin dropped from the roof (9:30)
Economics
marginal cost, revenue, and profit (7:04)
Exponential growth and decay
half life (8:06)
continuously compounded interest (2:50)
sales decline (6:07)
Final exam
calculus 1 final exam
introduction to derivatives
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