# Euclid's Muse

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# Search Results for “function-input”

By Duncan
##### Function Product Challenge 3
This time h(x) is unknown.  Can you find f(x) so that f(x)*sin(x) = h(x)?

Tags: functions

By Duncan
##### function product challenge 2
Can you find f(x) such that f(x)*g(x) = h(x)  (Yes, you could use f(x) = h(x)/g(x), but be more elegant!!)

Tags: functions

##### Moving point
We watch a point move according to a given displacement graph (which we can edit)

Tags: function, motion, displacement

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 Unit Circle
This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.

Tags: Geomtery, Unit-Circle, Sine, Cosine

##### 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.

Tags: Calculus, Derivatives, Functions

##### Application of The Mean Value Theorem to problem solving
Given function f(x) = (x+1)/(x-1). Show that there is no such c that f(3) = f'(c)(3-0). Why does this not contradict the Mean Value Theorem?

Tags: calculus

##### Application of The Mean Value Theorem to problem solving
Given function f(x) = arctan (1-x) on the interval [0, 1].

Tags: calculus

##### Application of Rolle's Theorem
Apply Rolle's Theorem to solve problems. Given function C(x) = 6(1/x + x/(x+4)).

Tags: calculus

##### 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?

Tags: Calculus, Defininte-Integral, Sine, Draggable