Define the sequence of functions {fn(x)} on (0, 1] by { 2n²x; 2n (1 — пх); 2п 2n fn(x) = 0; (a) Sketch on the same axis the graphs of fı(x) to f5(x). (b) Find f(x)= lim fn(x) . (c) Evaluate o f(x)dx (d) Evaluate fo fn(x)dx (e) Evaluate lim | fn(x)dx (f) Under which condition(s) will lim fn(x)dx = | lim fn(x)dx?

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…