## Calculus

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### Limits and continuity

Limits intro
Estimating limit from graphs
Estimating limit from table
Formal definition of limits
Properties of limits
Limits by direct substitution
Limits using algebraic manipulation
strategy in finding limits
Squeeze theorem
Types of discontinuities
continuity at a point
Continuity over an interval
Removing  discontinuities

### Derivatives: definition and basic rules

Average vs instantaneous rate of change
secant lines
Derivation Definition
Estimating Derivative
Differentiability
Power rule
Derivative rule : constant ,sum, difference and constant rule
Combining the power rule with other derivative rule
Derivative of cos(X),sin(X),In(x)
product rule
quotient rule
Derivation of tan(X),cot(x),sec(x), cos(x)
Proof video

### Derivatives: chain rule and other advanced topics

Chain rule
more chain rule
Implicit differentiation
Differentiating inverse function
Derivate of inverse trigonometric function \
strategy in different function
differentiations using multiple rule
second derivations
Disguised derivatives
Logarithmic differentiation
second derivative
Disguised derivatives
Logarithmic differentiation
proof video

### Applications of derivatives

Meaning of  the derivatives  in context
Straight in line motion
Non-motion application of derivatives
introduction  to related rates
Solving related rates problems
Approximation with local linearity
L ‘Hospital’s rule
L” Hospital :composite exponential functions

### Analyzing functions

Mean value theorem
Extreme value theorem and critical points
Interval on which a function is increasing or decreasing
Relative (local) extreme
Absolute (global)extreme
Concavity and inflection points intro
Analyzing concavity and inflection points
Second derivatives test
Sketching curve
Connecting f, “f” and f”
solving optimization problems
Analyzing implicit relation
Calculator-active practice

### Integrals

Accumulations of change introduction
Approximation with Riemann sums
Summations notations review
Riemann sums is summations notations
Defining integrals with Riemann sums
Fundamental theorem of calculus and accmulation functions
Interpreting the behavior of accumulations functions
Properties of definite integrals
Fundamental theorem of calculus and definite integrals
Reverse power rule
Indefinite integral of common function
Definite integral of common function
Integrating with u-substitution
Integral using long division and completing the square
Integrating using trigonometric identities
Proof videos
Differential equations
Differential equations Introduction
Verifying solution for different equations
Sketching solve field
Reasoning using slope field
Particular solutions to different equations
Exponential models
Applications of integrals
Average value of a function
Straight-line motion
Non -motion application of integral
Area: vertical area between curve
Area: horizontal area between curve
Area: curve that intersect more than between two points
Volume : Square and rectangles cross sections
Volume: triangle and semicircle cross section
Volume : disc method (revolving around x-and y-axes)
Volume : disc method (revolving around  other axes)
volume: washer method (revolving around x-and y-axes)

volume: washer method (revolving around other axes)

calculator active  practice.

### COURCE CHALLENGE

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.