When do we say that a function has a maximum and when a minimum?

When it has a global maximum at a point

When it has a global minimum at a point

Ποια θεωρήματα ισχύουν για το όριο και τη διάταξη;

ΘΕΩΡΗΜΑ 1ο: Αν lim f(x) > 0, τότε f(x) > 0 κοντά στο 0.

ΘΕΩΡΗΜΑ 1ο: Αν lim f(x)

ΘΕΩΡΗΜΑ 2ο: Αν οι συναρτήσεις f, g έχουν όριο στο 0 και ισχύει f(x) ≤ g(x) κοντά στο 0, τότε lim f(x) ≤ lim g(x).

Ποιες είναι οι ιδιότητες των ορίων;

lim f(x) = lim g(x) εφόσον lim g(x) ≠ 0.

lim kf(x) = k lim f(x) για κάθε σταθερά k.

lim f(x) * g(x) = lim f(x) * lim g(x)

lim f(x) + g(x) = lim f(x) + lim g(x)

What is the meaning of the limits lim x->∞ f(x) = L?

The values of f approach a real number L as x increases indefinitely.

The values of f approach infinity as x increases indefinitely.

The values of f approach negative infinity as x increases indefinitely.

What is the meaning of the limits lim x->∞ f(x) = +∞?

The values of f increase indefinitely.

The values of f approach a real number.

The values of f decrease indefinitely.

What are the properties of the infinite limit?

lim f(x) as x approaches 0 from the positive side equals +∞ if lim f(x) as x approaches 0 from the negative side equals +∞

lim f(x) as x approaches 0 from the positive side equals -∞ if lim f(x) as x approaches 0 from the negative side equals -∞

If lim f(x) as x approaches 0 equals +∞, then f(x) > 0 near x = 0, while if lim f(x) as x approaches 0 equals -∞, then f(x)

If lim f(x) as x approaches 0 equals +∞, then lim f(x) as x approaches 0 from the negative side equals -∞, while if lim f(x) as x approaches 0 equals -∞, then lim f(x) as x approaches 0 from the negative side equals +∞.

If lim f(x) as x approaches 0 equals +∞ or -∞, then lim f(x) as x approaches 0 equals +∞.

What are the limits of polynomial and rational functions at infinity?

For the polynomial function, the limit as x approaches +∞ is α.

For the polynomial function, the limit as x approaches -∞ is α.

For the rational function, the limit as x approaches +∞ is α/β.

For the rational function, the limit as x approaches -∞ is α/β.

What are the limits of the exponential and logarithmic functions at the ends of their domain?

If α > 1, then the limit as x approaches -∞ is 0.

If α > 1, then the limit as x approaches +∞ is +∞.

What is true about the image of an interval Δ of a continuous and non-constant function?

The image f(Δ) of an interval Δ through a continuous and non-constant function f is an interval.

The image f(Δ) of an interval Δ through a continuous and non-constant function f is a point.

The image f(Δ) of an interval Δ through a continuous and non-constant function f is a set of discrete points.

State the maximum and minimum value theorem for a continuous function.

If f is a continuous function on [α, β], then f takes a maximum value M and a minimum value m on [α, β].

If f is a continuous function on [α, β], then f is constant on [α, β].

If f is a continuous function on [α, β], then f has no maximum or minimum values.

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