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How do you intuitively remember the Lagrange Error Bound in AP Calculus BC?
I always get confused between alternating series error bound and the Lagrange error bound. What is the easiest way to determine the maximum value of M on the interval?
Think of the Lagrange Error Bound formula as the next term in the Taylor series, but replacing the derivative with M: |R_n(x)| <= (M / (n+1)!) * |x - c|^(n+1). Here, M is simply the maximum possible absolute value of the (n+1)-th derivative between your center c and target point x. For sine and cosine functions, M is always 1! Review complete formulas in our AP Calculus Formulas SheetAP Calculus AB & BC Prep Vault
Easiest method for calculating 30-degree conduit offset multipliers in the field?
When doing electrical conduit bending, what is the fastest mental math trick for a 30 degree offset?
The cosecant of 30 degrees is exactly 2.0! That means for any 30-degree offset, simply multiply the obstacle height by 2. If the obstruction is 6 inches high, the distance between your bend marks is exactly 6 * 2 = 12 inches with a shrink rule of 1/4 inch per inch of offset.
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