A gas tank contains 5.3 gallons. The capacity of the tank is 12.5 gallons. How much will it cost to fill the tank at $1. 30 per
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Answer:
The limit of the function does not exists.
Step-by-step explanation:
From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.
For x<2
The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.
For x>2
The value of y is 1 at x=2, because of he close circles on (2,1).
For x=2
Therefore the graph represents a piecewise function, which is defined as
The limit of a function exist at a point a if the left hand limit and right hand limit are equal.
The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.
Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.
A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as: p⇒q,
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
.
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that then Triangle ABC is not a right triangle with m(C)=90°
True
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that
True