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How can I distinguish when to use the verbs "ser" or "estar"?

Both these verbs are translates as "to be", however they are used in different circumstances. the verb "ser" is used to express permanent states of being, such as characteristics of ident...
HC
Answered by Hannah C. • Spanish tutor
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Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

y = e 2x (x 2 +1) 5/2 The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation: y = uv where u = e 2x and v = (x 2 +1) 5/2 . We now diffe...
AS
Answered by Adam S. • Maths tutor
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Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).

De Moivre's Theorem states that if z = cos(q)+isin(q), then z n = (cos(q)+isin(q)) n = cos(nq)+isin(nq) But then z -n = cos(-nq)+isin(-nq). Now, cos(-p)=cos(p), as cosine is a symmetric (even) function, and ...
DA
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Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Recall that for two lines to be skew they must satisfy two conditions: 1) They must not be parallel. 2) They must not intersect. We shall check each condition individually. Condition 1 The general vector equ...
DA
Answered by Dorian A. • Maths tutor
12255 Views

Prove that matrix multiplication is not commutative.

At GCSE level, proof questions are relatively rare and largely will all require a similar sort of approach. The difference with A Level is that the syllabus contains more than one method of proof. You will b...
SF
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