Task 2 gives you no sources and expects none. An example exists to make an abstract claim visible — to show what it looks like when it actually happens — and that is a genuinely useful job: a reader who has seen the claim in operation understands it better than one who has only been told it. What an example cannot do is establish that the claim is true, and the vocabulary has to respect that difference.
“A case in point is” and “for instance” illustrate. “Studies have proven that” and “according to a 2019 report” claim a source you do not have and cannot cite, and invented statistics are the most damaging version because they feel like rigour while you are writing them. An examiner who has read four essays quoting four different invented percentages reads the fifth exactly as what it is.
The grammar is small and worth getting right: “for example” takes a comma on both sides when it sits inside a sentence, and “such as” takes a noun with no comma at all. “For example of” does not exist — the phrase that does is “an example of”.
One concrete case makes the claim visible. It does not establish it, and no wording will.
“A recent study found that 73%…” is a fabricated fact and reads as one.
“For example” takes commas mid-sentence. “Such as” takes a noun and no comma.
A paragraph that is mostly example has stopped arguing.
