The sequence of functions {f,(x)} where fn(x) = x" converges on the interval [0, 1] to a function f(x). That limit function f(x) is O f(x)=0 for all 0sx<1 o for 0 sxs 1 f(x) =- [1 for exs1 2 O for 0 sx< 1 1 for x = 1 f(x) =- O none of the above

The sequence of functions {f,(x)} where fn(x) = x" converges on the interval [0, 1] to a function f(x). That limit function f(x) is O f(x)=0 for all 0sx<1 o for 0 sxs 1 f(x) =- [1 for exs1 2 O for 0 sx< 1 1 for x = 1 f(x) =- O none of the above

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

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 topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

The sequence of functions {f,(x)}where fn(x) = x" converges on the interval [0, 1] to a function f(x). That limit function f(x) is
O f(x) =0 for all 0< x<1
[o for o sxs
1 for 글 <xs1
f(x) =
0 for 0 sx< 1
1 for x = 1
f(x) =
O none of the above

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