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Search Results for “calculus”

By Aidan Wenzel
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

Tags: Ladder, Calculus, Derivatives, Pythagorean-Theorem

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

Tags: calculus

By Irina Lyublinskaya
Application of The Mean Value Theorem to problem solving
If f(2) = -2 and f'(x) >=2 for 2<=x<=6, how small can f(6) possibly be?

Tags: calculus

By Irina Lyublinskaya
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

By Phil Todd
Taylor series
Inspect the first three terms of the Taylor series of any function.

Tags: Taylor-Series, calculus, derivative, differentiation

By Phil Todd
Derivative
A graphical differentiation quiz

Tags: calculus, derivative

By Irina Lyublinskaya
Exploration of The Mean Value Theorem
Try different functions to explore The Mean Value Theorem.

Tags: calculus

By Irina Lyublinskaya
Applicaion of Rolle's Theorem
Apply Rolle's Theorem to solve problems.

Tags: calculus

By Nick Halsey
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


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