Gerunds and Infinitives + Polite Request

7.1.          Gerunds and Infinitives

We use gerunds (verb + ing):

·         After certain verbs - I enjoy singing

·         After prepositions - I drank a cup of coffee before leaving

·         As the subject or object of a sentence - Swimming is good exercise

      We use 'to' + infinitive:

• After certain verbs - We decided to leave
• After many adjectives - It's difficult to get up early
• To show purpose - I came to London to study English

We use the bare infinitive (the infinitive without 'to'):

• After modal verbs - I can meet you at six o'clock
• After 'let', 'make' and (sometimes) 'help' - The teacher let us leave early
• After some verbs of perception (see, watch, hear, notice, feel, sense) - I watched her walk away
• After expressions with 'why' - why go out the night before an exam?

7.2.          Polite Request

a.     Asking to do things – asking for permission

There are many different ways of making polite requests in English. If you don't want to sound rude when speaking English, then you need to know how to make a request in a polite way.Requests in English are usually made in the form of questions

Asking	Saying Yes	Saying No
Can I...?	Yes, sure	Well, I'm afraid...+ reason
Could I...? Could I possibly...? Is it all right if I...? Do you think I could...?	Yes, of course. Yes, that's fine. Certainly.	Well, the problem is...
Do you mind if I...?	No, not at all. No, of course not.	Sorry, but...

b.    Asking others to do things – making requests

Asking	Saying Yes	Saying No
Can you...?	Yes, sure.	Well, I'm afraid + reason
Could you...? Is it all right if you...? Do you think you could...? Will you...? Would you...?	Yes, of course. Certainly.	Well, the problem is Sorry, but...
Do you mind -ing...? Would you mind -ing...?	No, not at all. Of course not.

Use 'Would you mind if I...? Could I possibly...? Could you possibly...? Do you think you could...? to sound more polite.

Remember that 'Do you mind...?' and 'Would you mind...?' mean 'Is it a problem for you?' so the polite answer when we 'say yes' is 'No'.

Source :

http://www.perfect-english-grammar.com/gerunds-and-infinitives.html

http://www.ecenglish.com/learnenglish/lessons/polite-requests