Can you help me now? Could you do me a favour?

7. Both can and could with non-perfect infinitive are used in questions and statements to express offers and suggestions. These meanings can be further particularized as offering help, offering something, suggesting some arrangement, invitation etc.:

Offer:

Can / Could I make tea for you?

I could make tea if you want some.

Suggestion:

He could go out with us if he has nothing better to do.

Invitation:

You could join us at one of the weekends.

8. Could is used to express criticism or reproach for failing to do something that is expected. ‘ Could + indefinite infinitive’ is used if reproach refers to the present situation, ‘ could + perfect infinitive’ is used to express reproach for a past situation:

You could help me. You certainly could have told me about it.

9. Both can and could are used to express supposition (speculation) implying doubt and incredulity in interrogative sentences or surprise in special questions and almost assurance in negative statements. Indefinite and non-perfect continuous infinitives of the notional verb refer the action denoted by this verb to the present or future, while perfect forms of the infinitive refer the action denoted by the notional verb to the past:

Can you really believe it? How could you believe it?

Could she have really told him the details?

She cannot be working now. It's too late.

He couldn't have done it so quickly. It's absolutely impossible.

When the action denoted by the notional verb refers to the present, we often use the continuous infinitive to avoid ambiguity:

She can't work now.

(I am sure that she doesn't work now. She is not able to work now.)

She can't be working now. (I am sure she doesn't work now.)

As the negative form of the infinitive is not used in sentences expressing doubt and incredulity, other ways expressing negation are used. We can use phrases can it be that and it cannot be that or the verb fail followed by the indefinite infinitive of the notional verb:

Can it be that he doesn't know the facts yet?

It cannot be that she didn't want to see you.

Can he fail to understand what I mean?

She couldn't have failed to pass the test.

You can also express negation lexically:

Can she forget it (fail to remember)?

She couldn't have refused (not wanted) to help you.

Can you know nothing (not know anything) about it?

Depending on the situation the modal verb can have different meanings and the sentence can perform different communicative functions:

We could help you. Why didn’t you ask us? – Possibility

We could help you if we knew what you want. – Hypothetical possibility

We could help you. We are absolutely free now. – Suggestion

The form of the infinitive of the notional verb is closely connected with the meaning of the verb:

Could you do him a favour? – Request

Could you be doing him a favour? – Doubt

You cannot talk about it with strangers. – Prohibition

You cannot be talking about it with strangers. – Negative assurance

MAY

The modal verb may has two forms - may for the present and might for the past.

The modal verb may is used to express the following meanings.

1. The verb may is used with non-perfect infinitive to express formal permission when a speaker is asking for, granting or denying permission:

- asking for permission:

May I use the phone here?

- granting permission:

Yes, you may, if it is an emergency.

- denying permission (prohibition):

No, you may not. You may not use the telephone in my office.

The form might is used to express permission in clauses following the rule of the sequence of tenses: