learning curve

Examples of learning curve in the following topics:

• Tangent and Velocity Problems

  • Iinstantaneous velocity can be obtained from a position-time curve of a moving object.
  • In this atom, we will learn that instantaneous velocity can be obtained from a position-time curve of a moving object by calculating derivatives of the curve.
  • The green line shows the tangential line of the position-time curve at a particular time.
  • Recognize that the slope of a tangent line to a curve gives the instantaneous velocity at that point in time

• Impacts of Supply and Demand on Businesses

  • The supply curve goes in the opposite direction from the demand curve: As prices rise, the quantity of apples that farmers are willing to sell also goes up.
  • We do this by plotting both the supply curve and the demand curve on one graph.
  • The point at which the two curves intersect is the equilibrium price.
  • We've learned that without outside influences, markets in an environment of perfect competition will arrive at an equilibrium point at which both buyers and sellers are satisfied.
  • The demand curve would change, resulting in an increase in equilibrium price.

• Arc Length and Surface Area

  • Infinitesimal calculus provides us general formulas for the arc length of a curve and the surface area of a solid.
  • Determining the length of an irregular arc segment is also called rectification of a curve.
  • Historically, many methods have been used for specific curves.
  • The advent of infinitesimal calculus led to a general formula, which we will learn in this atom.
  • For a small piece of curve, $\Delta s$ can be approximated with the Pythagorean theorem.

• Long Run Supply Decisions

  • The long-run supply curve in a perfectly competitive market has three parts; a downward sloping curve, a flat portion, and an upwards sloping curve.
  • The long-run supply curve of a market is the sum of a series of short-run supply curves in the market ().
  • Prior to determining how the long-run supply curve looks, its important to understand short-run supply curves.
  • The producer has to incur fixed costs, such as learning the necessary skills to produce the item and purchasing new tools.
  • As a result, a long-run supply curve for a market will look very similar to short-run supply curves for a market, but more stretched out; the long-term market curve will a wider "u."

• Facts About the Chi-Square Distribution

  • When df > 90, the chi-square curve approximates the normal.
  • In the next sections, you will learn about four different applications of the Chi-Square Distribution.
  • Think about the implications of right-tailed versus left-tailed hypothesis tests as you learn the applications of the Chi-Square Distribution.

• Curve Sketching

  • Curve sketching is used to produce a rough idea of overall shape of a curve given its equation without computing a detailed plot.
  • Determine the symmetry of the curve.
  • If the exponent of $x$ is always even in the equation of the curve, then the $y$-axis is an axis of symmetry for the curve.
  • Determine the asymptotes of the curve.
  • Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve.

• History of the Normal Distribution

  • Abraham de Moivre, an 18th century statistician and consultant to gamblers, was often called upon to make these lengthy computations. de Moivre noted that when the number of events (coin flips) increased, the shape of the binomial distribution approached a very smooth curve.
  • de Moivre reasoned that if he could find a mathematical expression for this curve, he would be able to solve problems such as finding the probability of 60 or more heads out of 100 coin flips much more easily.
  • This is exactly what he did, and the curve he discovered is now called the "normal curve. "
  • The importance of the normal curve stems primarily from the fact that the distributions of many natural phenomena are at least approximately normally distributed.
  • The smooth curve is the normal distribution.

• Lab 1: Central Limit Theorem (Pocket Change)

  • Draw a smooth curve through the tops of the bars of the histogram.
  • Use 1 – 2 complete sentences to describe the general shape of the curve.
  • Draw a smooth curve through the tops of the bars of the histogram.
  • Use 1 – 2 complete sentences to describe the general shape of the curve.
  • Draw a smooth curve through the tops of the bars of the histogram.

• Lab 2: Central Limit Theorem (Cookie Recipes)

  • Draw a smooth curve through the tops of the bars of the histogram.
  • Use 1 – 2 complete sentences to describe the general shape of the curve.
  • Draw a smooth curve through the tops of the bars of the histogram.
  • Use 1 – 2 complete sentences to describe the general shape of the curve.
  • Draw a smooth curve through the tops of the bars of the histogram.

• Centripetal Force

  • A force which causes motion in a curved path is called a centripetal force (uniform circular motion is an example of centripetal force).
  • A force that causes motion in a curved path is called a centripetal force.
  • Previously, we learned that any change in a velocity is an acceleration.