MATEMATİK I - Deneme Sınavı - 12

Since a rational function f is continuous on the domain of its definition, f is continuous on its domain. the  is continuous for all real numbers x except -1 and 1. Thus, f is continuous on             R\{-1, 1}. The answer is B.

Let's denote the average velocity by V_a, denote the distance by X and denote time by t.

Then V_a=(X₂-X₁)/(t₂-t₁)=(300-140)/(4-2)=80

f(x)=(x²-5x+6)/(x²-9) = 0/0 which is indefinite for x=3. Thus we have to factorize the denominator and nominator of the function.

f(x)=(x²-5x+6)/(x²-9)=((x-3)(x-2))/((x+3)(x-3))=(x-2)/(x+3)

thus for x=3  lim f(x)=(3-2)/(3+3)=1/6

A function would be discontinuous when the value of function is undefined. In this case the values of x which make the denominator (x²-9) equal to zero will make the functiıon discontinuous. Thus for x=3 or x=-3, the denominator x²-9=0

We can take limits from left and right sides.

From left: lim f(x)=4-2*2=0

From right lim f(x)=2-2=0

So limit exists and it is equal to zero. This is obvious from the graph of the function:

For x=2:

the left limit of f(x)=9-x²=9-4=5=a

the right limit of f(x)=x-2=2-2=0=b

Then a-b=5-0=5

One can better understand from the graph of the function:

As you can see the function is discontinuous at x=2. So the left and right limits at that point are not equal to each other.

The biggest power in denominator must be higher than the biggest power in nominator for limit being equal to zero if x goes to infinity. So the answer is E as 3<7.

lim f(x)=lim (x²+3x+2)/((x²-x-6)=lim (x+1)(x+2)/(x-3)(x+2)=lim (x+1)/(x-3)=4/0=infinity

So the answer is A. In all other functions limit goes to a finite number.

(x³-8)/(x²-4)=(x-2)(x²+2x+4)/(x-2)(x+2)=(x²+2x+4)/(x+2)=19/4 for x=2. All other expressions are in the form of a/0 for x=2; which equals to infinity, and therefore not continuous. So the answer is C.

(x³-8)/(x²-4)=(x-2)(x²+2x+4)/(x-2)(x+2)=(x²+2x+4)/(x+2) which is infinite for only x=-2. Therefore the domain is R-{-2}