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  • Simulations
    • Ohm’s law simulation
    • Wave on a string simulation
  • Completing an ANOVA table
  • AP Calculus BC solved problem
    • Calculus Made Simple PDF
    • solved calculus bc math problems on arc length, differential equations and the integral of the second derivative
    • Limit x sin(1/x) as x goes to infinity
  • solved math problems
    • algebra
      • -2^3, -3^2,-4^3 (Examples of finding exponential expressions with negative bases and positive, whole number exponents)
      • (-2)^3,(-2)^2,(-3)^2 (Examples of finding exponential expression values)
      • 240 is 30% of what number?
      • A rectangular room is 3 times as long as it is wide
      • age problem algebra | algebra age problem
      • age problem involving number of years ago ages were equal
      • solving quadratic equations by using factoring (ac method with grouping, illustrated)
      • solving quadratic equations using the quadratic formula
      • solving quadratic equations by completing the square, no steps skipped
      • solving a radical equation with two radicals on one side
      • examples of solving equations with negative exponents
      • graphing a parabola by plotting points and connecting, graphing an absolute value graph by points
      • Ax+By=C facts and examples
      • graphing a line by xy intercepts and making the equation of a line from two points
      • two numbers add up to 33 and the difference is 77
      • simplifying experssions of the form a to the p over q
    • precalculus
      • domain and range of a square root function with a detailed graph and explanation
      • finding the domain and range of a square root function with a graph
      • domain and range of a quadratic function with a graph
      • domain and range of simple linear function
      • Find a polynomial of least degrees with real coefficients.
      • domains of functions examples
      • domain and range of an inverted quadratic function(negative leading coefficient)
      • finding the domain and range of a cubic function with a graph and a detailed explanation
      • solving rational equations examples with graphs
      • detailed examples of solving radical equations ,including using graphs
      • symmetry, even /odd functions, examples with graphs and detailed explanations
      • solving an inequality with three linear factors already in factored form (x+2)(x-3)(x+1) greater than or equal to 0
      • solving a radical equation by squaring and solving a quadratic quadratic equation with an extranous solution
      • solving a quadratic equation with complex roots detailed example with a graph
      • domain /range of a relation, evaluating functions with numbers and expressions, graphical domain and range of a function, vertical line test
      • examples of checking whether a function is even odd or neither
      • function composition example with value plugged in
      • function composition example with linear functions
      • solving a system of three linear equations step by step with annotations for better understanding
      • write a linear function to model a situation where w is the number of weeks and g w is the value in dollars on a card
      • sample solutions for 1.5 math 201 mercy fall 2021 average rate of change function graph comparing average rates of change
      • notes on multiplfying using foil and simple factoring factoring by grouping
      • detailed example of performing function transformation with reflections translations shifts
      • adding function, multiplying functions, dividing functions, subtrcting functions, rational functions, square root and linear function composition
    • calculus
      • relationship between the natural log and exponential functions and an application to derivatives
      • where are the graphs of x^2 and x^3 concave up/down?
      • concave up versus concave down
      • concavity of 1/x^2 with the second derivative
      • concavity of cubic polynomial
      • finding the concavity of sqrt(x) with the second derivative
      • finding the derivative of the absolute value of x
      • finding the derivative of |x-1| using the chain rule
      • examples of using the chain rule in calculus I
    • multivariable calculus
      • constructing a 3D coordinate system
      • sketching planes in three dimensional space
      • sketching a cylinder in 3D x^2+y^2=1
      • deriving the distance formula in three-dimensional space
      • deriving and using the equation of a sphere
      • region between two spheres
      • examples of inequalities in 3D
      • vector concepts
      • adding vectors
      • scalar multiplication of vectors
      • magnitude of a vector in 2D and 3D
      • forming linear combinations of vectors
      • unit vectors
      • decomposing a vector into components from the length and angle of the vector
      • finding the tensions in two ropes for a hanging object
      • dot product definition and properties
      • proof of Cauchy-Schwarz inequality, proof of Triangle Inequality
      • directions cosines for a vector in 3D
      • scalar , vector projections, work
      • distance from point to line using vectors, proof of formula, with several pictures
      • deriving the formula for finding the cross product of two vectors and vector product properties and applications with pictures
      • vector triple product proof and example
      • torque from vector cross product
      • equations of lines and planes in 3D, with examples and pictures, skew lines
      • equation of a plane in 3d formula and example
      • equation of a plane from three points in 3D
      • where does a line in parametric form cross a plane in 3D?
      • when are two planes in 3D space parallel (direction vectors are scalar multiples)
      • finding the angle between two planes using their direction vectors and the dot product, finding line of intersection of two planes
      • derive the formula for the distance between a point and a plane in 3D space
      • finding the distance between two skew lines in 3D space
      • cylinders and quadric surfaces
      • vector valued functions definition, domain examples
      • finding the limit of a vector-valued function, includes a graph and detailed calculations
      • identify the curve defined by a vector-valued function
      • constructing a picture of a toroidal spiral
      • concepts behind vector-valued function derivatives and an example
      • parametrizing a segment in 3D over 0<=t<=1
      • find parametric equations of tangent line in 3D find velocity vector and derivative of space curve
      • find the derivative and second derivative of a vector valued function at a point including a graph of the curve velocity and acceleration in three space
      • differentiation rules for vector-valued functions with proofs
      • reparametrize a curve example with a detailed explanation
      • integration of vector-valued functions, examples
      • arc length formula development and example for vector-valued functions
      • arc length integral in 3D development with an example for a helix raparametrization by arc length example
      • velocity and acceleration concepts and examples for space curves with projectile motion and tangential and normal components of acceleration using dot and cross products
      • multivariable functions, domains, ranges of graphs, level curves level surfaces definitions
      • examples of level curves for different types of functions.
      • example of limits in multivariable calculus one exists and one doesn’t exist
      • when does the limit of a multivariable function exist case of a functio of two variables
      • example of when a limit does not exist for a function of two variables 1
      • continuity of multivariable functions examples with detailed graphs
      • finding the limit of a function of two variables using polar coordinates
      • partial derivatives concepts graphs tangent lines examples
      • Understanding second partial derivatives with graphs
      • finding implicit partial derivatives examples
      • tangent plane approximations part 1
      • multivariable chain rule case 1 where z depends only on t with graphs
      • gradient vector meaning directional derivative level curves
      • max min concepts and examples in multivariable calculus
      • max min exampls with graph in multivariable calculus
      • max min examples in multivariable calculus 2
      • examples of max/min questions with lagrange multipliers
      • Finding a point of intersection between two planes.
      • solving a system of three linear equations, illustrated
      • calculus III notes
      • solving a system of three linear equations
      • examples of solving systems of equations with three variables
      • application of a system of three linear equations to investments
      • 3 by 3 Gaussian elimination two row operations applied in one step
      • 2 by 2 example and 3 by 3 example of solving systems using Gaussian elimination
      • using gaussian eliminination to show a system is inconstitent 3 by 3 and 2 by 2 examples with graphs of lines and planes
      • APPLICATION OF A GAUSSIAN ELIMINATINO TO SOLVING A SYSTEM OF THREE EQUATION WITH THEATER TICKETS
      • find specific combination of tofu, rice and peanuts to make a certain type of diet
        • solving a linear equation
        • pdf on identifying matrix columns, rows, doing matrix addition, subtraction
        • solving linear equation
      • solving sin squared plus cos x plus 1 equals 0 step by step with unit circle
      • Analysis of Rational Function
      • understanding the slope/derivative of e^x
      • linear dependence/independence for functions with examples
      • moving wave concepts illustrated with lots of graphs
      • rational function analysis
      • linear regression example found using matrices
      • best linear approximation
      • exponential function with a fraction in the base , horizontal asymptote, domain, range, points
      • discrete compounding sample calculations, continuous compounding included.
      • distance traveled by a particle found using calculus
      • solving simple differential equations with initial condition built into integral
      • Understanding Singularities in Complex Variables
      • two detailed examples of variations of parameters
      • Using a unit vector with tension.
      • detailed explanation of direction cosines
      • three examples of evaluating a piece-wise defined function
      • Vector Projections in 3D Space: Intuitive Explanations and Examples
      • How to graph 3D Vectors
  • Set Builder Notation Quiz

velocity and acceleration concepts and examples for space curves with projectile motion and tangential and normal components of acceleration using dot and cross products

velocity and acceleration concepts and examples for space curves with projectile motion and tangential and normal components of acceleration using dot and cross products

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