Tutor profile: Maia U.
What are some places that the subjunctive is used?
The subjunctive is used with some key phrases and ideas. In general, it is used when truing to convey any form of doubt of uncertainty. In general, it is a complex topic that even confuses native speakers and in some cases lacks a clear answer as to why something uses or doesn't use the subjunctive. The acronym WEIRDO is a good one to remember, W = Wants E = Emotions I = Impersonal Expressions R = Recommendations (/suggestions) D = Doubt/denial O = Ojalá (this one is just the word Ojalá which is loosely translated to "hopefully" and can be used in a multitude of contexts but always followed by the subjunctive).
How do you determine the charge on an ion For example, Nitrogen.
You must first look at the periodic table and find the column that nitrogen falls in. Each column, with the exception of the large block that is "sunken" in the middle of the table, has a specific charge. The column with H (hydrogen) at the top contains elements all with a +1 charge. Next, the column with Mg (magnesium) contains elements with a +2 charge. Skipping over the large section of metals in the middle, the next column that has a hard-and-fast-rule for charges contains Al (aluminum)--these ions all have a +3 charge. The next column containing C (carbon) either has a +4 or -4 charge, however this column specifically is not considered with determining ionic charges. The column containing N (nitrogen) is next, these elements having a charge of -3. The charges now continue to decrease with each column, followed by -2, -1, and finally 0 for the column containing the noble gases. A good way to remember this trend for ionic charges is count 1, 2, 3, 4 across and then decrease with -3, -2, -1, 0. Additionally, a good trick to memorize is to find Ag, silver, on the periodic table. Silver has a charge of +1. The diagonal that runs from Ag, to Zn, to Al also has a trend of charges for those THREE specific elements. Ag (+1), Zn (+2), and Al (+3).
How do you do basic implicit differentiation?
It involves the chain rule, which at its most basic form is taking the derivative of the entire function (ignoring any internal components) and then multiplying this answer by the derivative of the internal components. Specifically with relation to implicit differentiation, you take the derivative of each piece. The derivative of y is represented as f'(x) or dy/dx. This is so that the derivative as a whole can then by substituted in for f'(x), creating a function only in terms of one variable -- x. For example, f(x)=(x-y^3)^2 f'(x)=2(x-y^3)(1-3y^2*(dy/dx)) As seen above, the derivative of the whole function (x-y^3)^2 is taken using the chain rule. The inner part of the function remains unchanged and the derivative is just taken of the whole "outer" piece. Then, this is multiplied by the derivatives of the inner function. I say derivatives, because the rule of subtraction/addition applies where the full derivative is the sum/difference of the derivatives of the pieces. The derivative of x is 1 and the derivative of y^3 is (3y^2)(dy/dx). The dy/dx is included with the derivative of y because we must remember that the derivative of y is being taken in terms of x.
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