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Agreed. Learning is a drill-down process where you first get an overview and gradually break it down until you fully get it. It makes no sense to me to start with a very detailed account.jedishrfu said:I liked the hyperreals approach allowing you to skip the notion of limits initially in Calculus. Keisler's Calculus book goes that route and its arguably more intuitive to students initially than limits are.
https://www.math.wisc.edu/~keisler/calc.html
If we substitute ##n=1/h## and look for the ##a## for whichHallsofIvy said:Notice that C2C2C_2 is less than 1 while C3C3C_3 is larger than 1. So there exist a value of a, between 0 and 1 such that Ca=1Ca=1C_a= 1. We define "e" to be equal to that value of a. That is, dexdx=exdexdx=ex\frac{d e^x}{dx}= e^x.
SOHCAHTOA is a mnemonic device used to remember the trigonometric ratios of sine, cosine, and tangent. It stands for "Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent."
To use SOHCAHTOA, you must first identify which side of a right triangle is the opposite, adjacent, and hypotenuse. Then, you can use the mnemonic device to remember which trigonometric ratio to use to solve for the missing side or angle.
SOHCAHTOA is important because it helps us solve problems involving right triangles and trigonometry. It is a useful tool in fields such as engineering, physics, and navigation.
Some common mistakes when using SOHCAHTOA include using the wrong trigonometric ratio, not labeling the sides correctly, and forgetting to convert angles to the correct unit (degrees or radians).
SOHCAHTOA is limited to right triangles and cannot be used for other types of triangles. It also assumes that the triangle is in a two-dimensional plane and does not take into account three-dimensional objects.