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According to first principles, the differential is found as the limit as h->0 of:[f(x+h)-f(x)] / hif we set our f to x^2, then we find that this expression becomes (x^2+2hx+h^2 - x^2)/hWhich simplifies...
Given that w=xe-w use implicit differentiation to show that dw/dx = 1/(ew+x)Answer:Use product rule to simplify:dw/dx = x(de-w/dx) + e-w(dx/dx)Use ...
A) Since x, 12, y form a geometric sequence, we know that there exists some real number "r" (common ratio) such that 12=xr and y=12r. Hence, r= 12/x =y/12 => xy=144 => k=144 (cros...
When using proof by induction we most often prove a statement P for positive integers n. We think about the problem in a domino-toppling fashion. The first step is to write out P(n=1), so inserting 1 for ...
Let P(n) be the proposition that 2n+2 + 32n+1 is a multiple of 7 for all positive integers of n.Let n=123 + 33 = 8 + 27 = 35 = 7(5)This is divisible by 7....
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