To use X - X here has to be a tool, and to use X will mean do an activity where X will help or is needed to accomplish that activity. E.g.: Use the pen to write down what I say. A pen is a tool that is needed to accomplish writing.
To make use of X - This is like to use X except that X is not necessarily needed to complete the activity in question, but it will help. E.g.: Feel free to make use of anything in my spice rack when you start cooking. The spices might help, but aren't strictly required.
To tap into X - A physical tap is something that allows one to draw out or extract water, liquid, or other similar resource from a stream, network, or container. Following this logic, tapping into something can mean attempting to draw out or extract something needed (from someone) that can help you complete an activity, and this something will not be a physical object but a mental resource such as knowledge, skill, social connections, etc. Tap into your customer service skills when dealing with difficult requests.
So ...
A market in my opinion at least, that can be tapped into. Graduates would more likely be something made use of unless your location is starved for the skills of this specific group of graduates. Tap into X somewhat carries the subtext of X is needed by us but not vice versa.
And,
Can you make use of these papers?
Can you use these papers?
The difference in meaning depends on what the papers contain and how useful they are to the person you are offering to them. If you think they will help, but aren't required, make use of is appropriate. If you think they are needed by him to accomplish his task, use is appropriate.
The phrase
I'll let you know
us usually used to tell someone they'll keep you updated on a decision or situation.
Other phrases that can be used are
I'll tell you as soon as I know
I'll keep you updated
I'll keep you posted
Your second phrase
I'll give you a shout
usually only means someone will contact you regardless of the situation and may or may not have the same meaning as "I'll let you know", it would depend on context and custom.
I'll give you a shout and let you know when I find out.
I'll give you a shout to arrange meeting up later this week.
Best Answer
In the same way as
requires "to",
requires the bare infinitive without "to".
The "rule" is what I have said just above: it is an idiosyncratic property of the verb "let", that cannot be predicted but just has to be learnt.