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Troubleshooting: Evaluating an Trigonometric Integral Algebraically

Hehe…we are always amused by calculus students who manage to mis-integrate a function to the point of yielding nonsensical answers. To illustrate what we mean by this, here is Steve, who — at the point of this writing at least — still haven’t got a clue where his computations went awry: How do you evaluate […]

Modular Arithmetic — Some Advanced Tricks in Finding The Least Positive Residue

We got a least-residue question from David a few weeks ago, but never took the time to address it properly. While procrastination and busyness can take a toll on us, at some point one still needs to face the reality and get things done promptly (don’t you think, students? ðŸ˜‰ ). OK. Enough said. Here’s […]

Solve The Following System of Linear Equations With An Additional Parameter

Today, Connor asked the following question involving a system of linear equation with an additional parameter: Given that $x_1 + hx_2 = 4$Â  and $3x_1 + 6x_2 =8$, find all pairs of the form $(x_1,x_2)$ satisfying both equations. OK…What do we do with that additional $h$? Well, read on!

Solving the Triangle with A=30Â°, b=40, and a=10

We got asked this trigonometry question, which we immediately converted into drawing for better readability. Before we begin, what does it mean to solve a triangle? Well, it’s just a short way of saying findingÂ all the missing side lengths and angles of a triangle. So how on earth do you solve this triangle, with only […]

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