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A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 19 feet from the wall. Round your answer to three decimal places. ​ ​

Find  at the point for the equation. ​

Given the derivative below find the requested higher-order derivative. ​ , . ​

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the position of the object when . Round your answer to two decimal places. ​

Find  if . ​

Find the slope of the graph of the function at the given value. ​ at ​

Find the derivative of the following function using the limiting process. ​

Find an equation to the tangent line for the graph of f at the given point. ​ , ​

A ladder 25 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is 11 feet from the wall. Round your answer to two decimal places. ​ ​

Find the slope of the tangent line  at the given point . Round your answer to two decimal places. ​