Mathematics 1 Dersi 5. Ünite Sorularla Öğrenelim

What is Calculus interested in ?

Calculus is interested in motion and change of quantities that depend on certain parameters through a rule. For example, the change of velocity of a car with respect to time, change in temperature with respect to the temperature of the surrounding environment, growth of a certain amount of money with respect to interest rate are only a few that comes to mind.

What are two fundamental concepts of Calculus?

It has two fundamentally significant concepts.The first of these concepts is the derivative, that is finding instantaneous change of a given function at a given point. It corresponds to the problem of finding the slope of a line tangent to a given curve at a given point on the curve. The second problem is concerned with finding the area of a plane region bounded by given curves. The solution of the problem of areas is the subject of the integral concept. 

Suppose that a ball is dropped from the top of a tower of height 200m. What equation gives us the distance of the ball travels in the first t seconds?

Suppose that a ball is dropped from the top of a tower of height 200m. In the first t seconds, the distance of the ball travels is given by the equation
y (t)= 4,9t².

What is the tangent line problem?

The tangent line problem is the problem of finding a line that is tangent to a given curve (circle, graph of any function, etc.) at a given point P on the curve.

What does ’x?x0’ mean in the definition of limit?

Let us note that the expression ‘’x?x₀’’ in the definition of limit means that even though f may not be defined at the point x₀, we can make the value of f (x) as close as we want to L.

What does the limit of a function at a given point x₀ determine? 

The limit of a function at a given point x₀ determines the behaviour of the function near x₀.

What do the symbols –? and +? represent ?

The symbols –? and +? do not represent numbers. They imply unbounded behaviour.

What do continuous on the interval and a continuous function mean?

If a function f is continuous at every point of the interval I, where it is defined, we say that f is continuous on the interval I. Also, if f is continuous at every point of its domain of definition, we say that f is a continuous function.