Parabola, Tangent to parabolas and Taylor Polynomial of sin(

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• Parabola

  Show that the tangents at P and Q intersect on the directrix of the parabola Please see the attached file. This is a problem regarding tangent and focus of a parabola. Parabolas which pass through the focus are determined.

• Find point of intersection of two lines tangent to a parabola

  Find the equations of the tangent lines to the parabola at the points P and Q, as well as their point of intersection. Show that those two tangent lines intersect on the directrix of the parabola and are at right angles to each other.

• Real-Life Applications of Hyperbolas and Parabolas

  Or you could say that the slope of the tangent line to the parabola at the point having any given x-coordinate will be greater than the slope of the tangent line to the hyperbola having the same given x-coordinate.

• Applications of Parabolas and Hyperbolas: Real-Life Applications of Probability

  Or you could say, given the x-coordinate, the slope of the tangent line to the parabola at the point will be greater than the slope of the tangent line to the hyperbola. 1.

• Parabolas and Complex Roots

  151209 Parabolas and Complex Roots How many times does the graph of a quadratic equation (a parabola) cross the x-axis?

• Taylor Polynomial for a Sine Function

  137257 Taylor Polynomial for a Sine Function Find the Taylor polynomial of order 3 for f(x) = sin x, centered at Xο = pi/2 (Xο ο is a subscript) As f(x) = sin x, we have f'(x)=cosx, f"(x)=-sinx, f"'(x)=-cosx Hence,

• Taylor polynomials

  This shows how to find a Taylor polynomial and plot the function and polynomial.

• General Calculus Questions : Definition of a Limit and Derivative, Product Rule, Tangent Line Approximation, Taylor Polynomial, Newton's Method, L'Hopital's Rule, MVT, IVT, Fundamental Theorem

  What is the Taylor polynomial approximation to a function? Explain how to use tangent line approximation of the derivative of a function to get a quadratic approximation to the function . Solution.

• Pade (Rational Function) Approximation

  Pade or rational functions are similar to approximations by Taylor polynomials. The method of finding a rational function from a given Taylor polynomial is described and several examples are worked in detail.