Answer:
The answers are indeed
1. gerund
2. infinitive
3. participle
Explanation:
In the first sentence, "Climbing a rope is not as difficult as you might think," the subject is "climbing a rope". Climbing is the most important part of this subject. For the word "climbing" to be a subject, it must function as a noun in the sentence. The verb+ing form that functions as a noun is the gerund. Therefore, "climbing" is in the gerund.
In the second sentence, "I plan to compete in a chess tournament this weekend," the most important part of the object of the verb "plan" is "to compete". "To compete" is also functioning as a noun, but this time the verb form is to+verb, which is an infinitive.
In the third sentence, "Kali loves the smell of roasting garlic," we have a verb+ing form again. This time, however, "roasting" is not functioning as a noun, but as an adjective. It modifies the noun "garlic". In this case, we have a present participle form.