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### Questions (6)

 4 $\sum x_n$ and $\sum y_n$ converge, show $\sum (x_n + y_n)$ converges 2 Prove that the translation of an integrable function is also integrable. 2 Prove Lipschitz function $f$ with constant $K$ is integrable on $[0, 1].$ 1 If a function $f(x)$ is Riemann integrable on $[a,b]$ and $|f(x)| \le M$ for $x \in [a, b]$, show $|\int_a^b f(x)dx| \le M(b - a).$ 0 Show $f$ is constant zero function on $[a, b]$ if $\int_a^x f(t) dt = \int_x^b f(t) dt \forall x \in [a, b].$

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### Tags (9)

 0 real-analysis × 6 0 sequences-and-series 0 integration × 5 0 convergence 0 riemann-integration × 3 0 lipschitz-functions 0 calculus × 2 0 derivatives 0 riemann-sum × 2

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