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Mathematics 1 Dersi 5. Ünite Sorularla Öğrenelim

Limits And Continuity

1. Soru

What is Calculus interested in ?

Cevap

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.


2. Soru

What are two fundamental concepts of Calculus?

Cevap

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. 


3. Soru

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?

Cevap

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.


4. Soru

What is the tangent line problem?

Cevap

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.


5. Soru

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

Cevap

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.


6. Soru

What does the limit of a function at a given point xdetermine? 

Cevap

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


7. Soru

What do the symbols –? and +? represent ?

Cevap

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


8. Soru

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

Cevap

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.


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