…a person in calculus might be led to believe that the following are true?
- The graph of the derivative of f(x) is just the graph of f(x) turned upside down.
- Dividing by x is the same thing as subtracting x, as in: (1 + x2)/x = 1 + x2 – x.
- Update: Dividing by x is the same thing as changing the exponent to -1 and adding, as in: (1 + x2)/x = 1 + x2 + x-1.
- ln(x) = 1/x.
I’m getting these on the final exams I am grading right now; I got them from some of the students throughout this course and have gotten them before in every calculus class I’ve taught going back for years. I can see how students might get screwed up on the third point, but the first two are just inexplicable — there’s nothing that would cause a person to think this, at any level of math.
Updates will follow as I encounter more “new math”. Hopefully that means no more updates. (Update: Oh well.)
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