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First we establish our base case: f(0) = 2² + 3¹ = 4 + 3 = 7, so clearly f(0) is divisible by 7.Now. by the inductive hypothesis. we assume that f(k) is divisible by 7, and attempt t...

We'll apply the quotient rule using "u = ln(x² + 1)" and "v = x² + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see &quo...

I come from Leipzig, a city in the east of Germany. Before I was born, Germany was divided - the Federal Republic of Germany and the German Democratic Republic. There were two different political systems ...

(i) 5 peaks (ii) 3 peaks(iii) 4 peaks

y^-1 dy = xcos(x) dx∫y^-1dy = ∫xcos(x) dx ln(y) = ∫xcos(x) dx [using integration by parts to integrate the right hand side] therefore, ln(y) = xsin(x) - ∫sin(x) dxln(y) = xsin(x) + cos...