Search Results for “Calculus-A/B”
Sliding Ladder Problem
One of the first calculus class problems is the sliding ladder. In this problem, a ladder is resting against a wall when, all of a sudden, it starts sliding down! In this problem you're solving for dx/dt or the rate at which the point B is moving away from the wall (point C). Input constraints: -The rate of slide must be negative for the ladder to slide down -The initial height of the ladder must be less than the ladders length
Basic Derivatives
Drag the point to see how the slope of the line relates to the x value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the x and y coordinates? The slope of the line can also be represented in terms of x; can you figure out what this representation is? This representation is the derivative of the entire function, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of F(x) = F’(x), although there are many other notations as well.
Area Under Sine (draggable)
Observe the definite integral of sine, or the area between the function sin(x) and the x axis, and how it changes between different bounds by dragging the boundaries, a and b. What happens to the area when the interval is 2Π? Why?
Vector Combinations and Span
AB and AC are vectors. Vector AF is defined by t(AB) + s(AC) where t and s are scalars. Drag E and D to change the scalars and see how using the scalars creates vectors in the plane defined by AB and AC.
Application of Rolle's Theorem
Apply Rolle's Theorem to solve problems. Given function C(x) = 6(1/x + x/(x+4)).
