This is a problem from ISI MStat 2019 PSA Problem 16 based on calculating area bounded by the curve Area bounded by the curve – ISI MStat Year 2018 PSA Problem 16 The functions \(f, g:[0,1] \rightarrow[0,1]\) are given by \( f(x)=\frac{1}{2} x(x+1)\) and \(...

This is a problem from ISI MStat 2018 PSA Problem 11 based on Sequence Sequence & it’s subsequence – ISI MStat Year 2018 PSA Problem 11 Let \( {a_{n}}_{n \geq 1}\) be a sequence such that \( a_{1} \leq a_{2} \leq \cdots \leq a_{n} \leq \cdots\)Suppose...

This is a problem from ISI MStat 2018 PSA Problem 8 based on limit of a function Limit of a Function – ISI MStat Year 2018 PSA Problem 8 The value of \( \lim _{x \rightarrow \infty}(\log x)^{1 / x} \) (A) is e(B) is 0(C) is 1(D) does not exist Key Concepts Limit...

This is a problem from ISI MStat 2018 PSA Problem 10 based on limit of a function Dirichlet Function – ISI MStat Year 2018 PSA Problem 10 Let \(x\) be a real number. Then \( \lim {m \rightarrow \infty}\left(\lim {n \rightarrow \infty} \cos ^{2 n}(m ! \pi...

This is a problem from ISI MStat 2018 PSA Problem 7 based on Continuity Continuous Function – ISI MStat Year 2018 PSA Problem 7 Let \(f\) be a function defined from \( (0, \infty)\) to \(\mathbb{R}\) such that\( \lim _{x \rightarrow \infty} f(x)=1\) and \(...

This is a problem from ISI MStat 2018 PSA Problem 12 based on Sequence of positive numbers Sequence of positive numbers – ISI MStat Year 2018 PSA Problem 12 Let \(a_n \) ,\( n \ge 1\) be a sequence of positive numbers such that \(a_{n+1} \leq a_{n}\) for all n,...