There's some nuanced differences between the two. I came to know implies a more lengthy, substantial or involved process of acquiring knowledge than I learned. Synonyms of come to know include come to understand and become acquainted with, which are a little more distant from learn. For example, I came to know calculus suggests a drawn out process or a deeper, more personal relationship with the subject than I learned.
I don't know of any instances where I learned cannot be validly replaced by I came to know, but I do know that the exchange doesn't always work in the other direction. I came to know my neighbor is fine, but I learned my neighbor is unsemantic (people are not facts or ideas; you cannot learn them). I discount learned a lesson here because it carries a very specific meaning and uses learn in a different sense than usual. Cambridge even lists it as a phrasal verb (or at least thinks it merits a separate entry).
However, your question includes that after both phrases. Having that makes it about some particular pieces of information. In this case, came to know is a superset of learned, because both are completed processes of acquiring knowledge, and learning is about retaining specific facts. Because of this, I can't think of any cases where one works and the other doesn't if you include that.
Regarding your example, what's the context? Was the discovery of this information expedient and easy? Is the sentence intended to be merely informational? If so, use learned. Was it very difficult or time consuming to find out the woman's status? Is it the knowledge extremely important and worth emphasizing? Are you trying to avoid being prosaic? If so, use came to know. Compare:
I flew to Bangladesh to see my cousin. After landing, I went to a restaurant to meet her and her husband. Upon arrival, I learned that she was not in town. She had to make a business trip and would return the following week.
Tracking the billionaire's wife across Europe was no easy task, but I finally found out she was in Madrid, so I double timed it over there. Upon arrival, I came to know that she was not in town. I asked around at the likely clubs and bribed clerks at the upscale hotels, but if anyone had seen her they weren't talking.
Section, segment, or part all have similar meanings, but the situations in which each can be used is different.
According to Oxford Dictionaries Online, a section is
- Any of the more or less distinct parts into which something is or may be divided or from which it is made up
- A distinct group within a larger body of people or things
Therefore, you only use section when the larger thing that the section is coming from can be, or is, divided into distinct parts.
According to Oxford Dictionaries Online, a segment is
- Each of the parts into which something is or may be divided
- Geometry A part of a figure cut off by a line or plane intersecting it, in particular
Thus, a segment is almost exactly the same as a section, and the two can be used interchangeably. However, segment carries a secondary meaning and so can also be used when specifically talking about lines and planes in geometry.
When you look up the word part in Oxford Dictionaries Online, you'll find that it has no less than 15 different meanings and submeanings. It is therefore the most broad and flexible of the three words we're studying, but it's general meaning is
An amount or section which, when combined with others, makes up the whole of something
So you can use part whenever you want to talk about any piece of a larger entity.
In terms of your examples...
"That segment/section of the road is still closed." Segment and section are interchangeable here. In my experience, section would be the most commonly used, but segment is equally valid, especially since a road is more or less a line, and in geometry we have line segments. You can also use part, but you lose the specificity you would have had with the other choices.
"The library has a large biology section." This is a special case. Section is the only acceptable word to use here. The biology section is a distinct part of the larger library. I have only ever heard people using section to reference specific areas of libraries, never segments, or even parts. And I've been in a lot of libraries.
"The tail section of the plane." Section is the most common word to use in this case. You can also say part, if you want to give a more informal tone.
Best Answer
It might help to see "extrapolate" as a sub-type of "infer."
"Infer" can refer to small abductions that aren't always as well supported. One can infer emotions in the speaker, but not extrapolate emotions. It's not uncommon for a heated discussion to feature an accusation of "You implied (X)!" and response of "I did not! You inferred that!"
"Extrapolate" generally refers to statistical or logical inferences and tends to indicate a more scientific and controlled context. The product of extrapolation (the extrapolated information) is generally larger quantitatively or qualitatively, whereas "infer" can be is more limited. The etymology of "extrapolate" points to looking at patterns within some set and reproducing those patterns outside the set as a prediction, which should reinforce that "extrapolate" is a term used in more logical and quantitative speech.