Calculus at University
The study of calculus usually starts at the high school level, with concepts like the derivative and the integral being introduced to students. At the university level, we cement this subject by studying real analysis. We rigorously explore and define ideas such as sequences and series, continuity, integrability, convergence and so on.
In my first few lectures as a second-year mathematics student at Warwick University, I looked at the idea of pointwise limit and pointwise convergence.
In simple terms, the pointwise limit of a sequence of functions is the function f(x) to which the sequence converges for each individual point x in the domain.
It differs from ordinary limits in that we do not only consider the limit of a sequence of numbers but rather the limit of a sequence of functions. We are trying to a function f(x) that acts as the limit for the sequence of functions fn(x) at each point x in the domain.
In today’s question, we have to consider the domain [0 to infinity). Let’s give this problem a try before jumping in for the solution!
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