Some verbs have their objects take either to-infinitive or gerund form without change in meaning:

            After a short while, the journalists began to ask questions

            After a short while, the journalists began asking questions.

A list of such verbs are:

            begin                            bother                          can/cant' bear

            cease                            continue                        fear

            intend                           propose                        start

            like/dislike                    omit                              neglect

            can't stand

We make exemplary sentences in pair in the following: 

1.         They don't even bother to make any more effort to persuade him.

            They don't even bother making any more effort to persuade him.

2.         He can't bear her ignoring him.

            He can't bear for her to ignore him.

            She can't bear losing any single game.

            She can't bear to lose any single game.

3.         We ceased to attack our opponents.

            We ceased attacking our opponents.

4.         We'll continue to debate the pros and cons of this issue.

            We'll continue debating the pros and cons of this issue.

5.         Having not prepared sufficiently, I feared to take the exam.

            Having not prepared sufficiently, I feared taking the exam.

6.         He intended to come to help, but she kicked him away.

            He intended coming to help, but she kicked him away.

7.         She proposed to go to beach and have a picnic there.

            She proposed going to beach and having a picnic there.

8.         We'll start to lecture at 8:30 in the morning.

            We'll start lecturing at 8:30 in the morning.

9.         They dislike to play tennis in the late evening.

            They dislike playing tennis in the late evening.

10.       He omitted reading the second page.

            He omitted to read the second page.

Well, although we said that with gerund or infinitive, the meaning of the sentence won't change, the delicate differentiation exists for some of the verbs listed above:  gerund is used more for statements in general, while infinitive is more for a specific situation, for example,

            I like going to trade fairs (trade fairs in general).

            I like to go to the trade fair tomorrow (one specific trade fair).

We could make a sub-list of such verbs:

            hate                  like                   love                  prefer               dread

Examples for each of the verbs listed above are:

1.         We hate eating noodles as breakfast (more general)

            We hate to eat noodles as breakfast this morning (more specific.  We may like noodles, but just don't want to have noodles this morning).

2.         She loves playing tennis (more general).

            She loves to play tennis with him this morning (more specific.  She just likes to play with him today.  It may or may not be the case at any other times.)

3.         He prefers not playing her (more general.  Does not want to play her any times). 

            He prefers not to play her this afternoon (more specific.  Does not want to play her, at least not this afternoon).

4.         He dreads to go.

            He dreads going (use of the infinitive is generally preferred).

5.         I like swimming (more general, I like swimming as a sport).

            I like to swim this afternoon (more specific,  I may just like to do that this afternoon)[1].

Another sub-list of verbs with either gerund or infinitive has a different feature:  when there is no other object, use the gerund;  when there is another object, use the infinitive, for instance:

            We allow smoking here.

            We allow our personnel to smoke here.

This sub-list is

            advise               allow                encourage                     recommend

You may also want to take a detailed look at the following paired exemplary sentences:

1.         She wanted to advise him to calm down. 

            She wanted to advise calming down. 

2.         He encouraged her to make a serious effort on her manuscript.

            He encouraged working hard as an ethical and behavioral habit.

3.         We would recommend you to consider him the top candidate for the position.

            We would recommend considering him the top candidate for the position.

Some other verbs are also followed either by gerund or to-infinitive, however, the meaning of the sentence will be different (could be very different).  Let's look at them one by one[2]:

1:          Do you remember giving the document to the secretary yesterday?

             Will you remember to give the document to the secretary tomorrow?

The first sentence refers to the past.  The action "giving" was done and you are asked whether the fact is retained in your memory.  The second sentence refers to the future.  The action "to give" is yet to be done and you are asked whether your memory will be able to remind you to complete this action in the future.

2:         We stopped eating at 9 p.m. last night.

            We stopped to eat at 9 p.m. last night.

The first sentence says that we no longer ate after 9 p.m. last night (the action of "eating" was stopped at 9 p.m.).  The second sentence states that we stopped what we were doing (or paused, say, on our way home) and started to eat at 9 p.m. last night ( we can think of two actions were involved:  the first action that was stopped was implicit and not shown in the sentence, then the second action got started as soon as the first implicit one was stopped).

3:         The speaker went on talking about his favorite subject for the whole morning.

            After his formal speech, the speaker went on to talk about his favorite subject.

The first sentence expressed that the speaker continued with the same action, while the second sentence started his favorite subject (another action), after his formal speech was done (one action).

4.         This machine needs to be repaired.

            This machine needs repairing.

Here the literal and actual meaning is the same, but after the verb need, if infinitive is used, then the infinitive must be of the passive voice; if gerund is used, then the gerund must be in the active voice.

5:         Sorry, I did not mean to hurt your feeling.

            Committing ourselves to this plan means working 3 hours every day.

In the first sentence, mean = to intend.  In the second sentence, mean = to have a consequence, to entail.

6:         I regret to inform you that we'll have to put you on the waiting list.

            I regret using my time unwisely when I was in college.

In the first sentence, "regret to (do)" means the action yet to be done although the person (subject) is unwilling to do, but has to do (a somewhat futuristic action).  In the second sentence, "regret (do)ing" mean "to feel sorry for something that happened in the past and even to wish to have done that otherwise".

7:         He'll try to solve those grammar problems this afternoon.

            He tried solving those grammar problems last night.

In the first sentence, "try to (do)" implies an action that the person (subject) is about to attempt (futuristic).  In the second sentence, "try (do)ing" indicates the process of the action that the person has already started (but frankly, I believe that the difference is not obvious between these two sentences).

8:         He forgot doing this problem before.

            He forgot to do the homework last night.

In the first sentence, "doing this problem before" happened before, but the subject (person) did not retain this action in his memory.  In the second sentence, "to do the homework" is the action the subject person is supposed to do but did not.

9:         He attempted to lie.

            He attempted lying.

Use of the infinitive is more forceful and carries a stronger sense of action than use of the gerund.  But the two forms are equally acceptable.