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Find the Taylor polynomial of degree 4 at c=1 for the equation and determine the accuracy of this polynomial at x=2.
The quarterback of a football team releases a pass at a height of 7feet above the playing field, and the football is caught by a receiver 30 yrds .
Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5
The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)
If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives.
Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives.
The equation x2 - 3x + 1 = 0 has a solution for x = 0. Give the third approximationby using Newton's method. Your first approximation is to be 1.
Let f: I ?R where I is an open interval containing the point c, and let k ? R. Prove the following.
Differentiate to derive the equation for instantaneous velocity, which would be represented by the gradient of a graph.
Determine whether the function is homogenous. If it is, state the degree.Provide complete and step by step solution for the question and show calculations.
Find the mass and centroid of the plane lamina with the indicated shape and density.
A tank is in the shape of an inverted cone (pointy at the top) 6 feet high and 8 feet across at the base. The tank is filled to a depth of 3 feet.
At 8am on Saturday, a man begins running up the side of a mountain to his weekend campsite. On Sunday at 8am, he runs back down the mountain.
Show that the rate of change of the volume of water in the container due to evaporation is directly proportional to the exposed surface area of the water.
The graph of g passes through each of the points (x,f(x)) given in the table above. Is it possible that f and g are the same function?
An ant is walking around the outside of the cube in "straight" paths (where we define a straight path in this case as one formed by the edges.
Find the volume of the solid generated when the enclosed region of f and g between x = ½ and x = 1, is revolved about the line y = 4.
Make a conjecture, on the basis of physical reasoning, as to whether you expect the amount of salt in the tank to reach a constant equilibrium value.
Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process.
If 2 subintervals of equal length are used, what is the midpoint Reimann sum approximation of integral with 5 on top and 1 on bottom f(x)dx?
Let f be a differentibale function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that.
Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)
A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north.
What is the terminal velocity vT=lim as t approaches infinity of a 100-kilogram object (a small linebacker or a large flower pot) subject to air resistance.
Find the critical points and use your test of choice to give local maximum and minimum values. Give those values.