The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. What is…

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In his paper The Transition to Formal Thinking in Mathematics, David Tall presents W.P. Thurston’s seven different ways to think of the derivative: Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function. Symbolic: the derivative of x^n is nx^n−1, the derivative of sin(x) is cos(x), the…

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