Here, the notation
refers to negative infinity, and it indicates that we are including all numbers less than or equal to zero, no matter how small. The set
refers to the set of all real numbers.
Some functions are defined using different equations for different parts of their domain. These types of functions are known as
piecewise-defined functions . For example, suppose we want to define a function
with a domain that is the set of all real numbers such that
for
and
for
We denote this function by writing
When evaluating this function for an input
the equation to use depends on whether
or
For example, since
we use the fact that
for
and see that
On the other hand, for
we use the fact that
for
and see that
Evaluating functions
For the function
evaluate
Substitute the given value for
x in the formula for
For each of the following functions, determine the i. domain and ii. range.
Consider
Since
is a real number for any real number
the domain of
is the interval
Since
we know
Therefore, the range must be a subset of
To show that every element in this set is in the range, we need to show that for a given
in that set, there is a real number
such that
Solving this equation for
we see that we need
such that
This equation is satisfied as long as there exists a real number
such that
Since
the square root is well-defined. We conclude that for
and therefore the range is
Consider
To find the domain of
we need the expression
Solving this inequality, we conclude that the domain is
To find the range of
we note that since
Therefore, the range of
must be a subset of the set
To show that every element in this set is in the range of
we need to show that for all
in this set, there exists a real number
in the domain such that
Let
Then,
if and only if
Solving this equation for
we see that
must solve the equation
Since
such an
could exist. Squaring both sides of this equation, we have
Therefore, we need
which implies
We just need to verify that
is in the domain of
Since the domain of
consists of all real numbers greater than or equal to
and
there does exist an
in the domain of
We conclude that the range of
is
Consider
Since
is defined when the denominator is nonzero, the domain is
To find the range of
we need to find the values of
such that there exists a real number
in the domain with the property that
Solving this equation for
we find that
Therefore, as long as
there exists a real number
in the domain such that
Thus, the range is
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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