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For N to be not divisible by 3, N can either be of the form 3k + 1 (1,4...) or 3k + 2 (2,5...), where k is an integer.
The proof can then be done by checking both 3k + 1 and 3k + 2 when N is squared...

f'(x)=lim(h->0) of [f(x+h)-f(x)]/h. In the case where f(x)=x^n, we have that f(x+h)-f(x)=h*nx^(n-1) + (h^2)*p(x) for a polynomial p(x), shown by binomially expanding f(x+h). Then dividing through by h ...

We are given that f(x) = 1/x - sqrt(x) + 3. Here, f(x) represents a function. A function is a relation or expression involving one or more variables. We are able to differentiate f(x) in order to find the...

First rewrite the equation into an easier form:y = y = 4x^3 - 5x^-2dy/dx means differentiate y with respect to xSo when differentiating, you look at the first term and write the co-efficient of the x term...

f(x)= xsin(x) >>>>>>>>>>>>>>>>>> integral[ udv/dx ] dx= uv - integral[v* du/dx] dx
let x=u and sin(x)=dv/dx >>>>>>>...