What is the rate at which reciprocal of a number changes with respect to the number if the number is equal to 7? Let n be the number and r be the reciprocal of the number?
r = 1/n
dr/dt = -n^2 dn/dt
when n = 7, r = 1/7
dr/dt = -49 dn/dt
we have missing information
r = 1/n
dr/dn = -1/n^2
...
To find the rate at which the reciprocal of a number changes with respect to the number, we can use calculus. Let's start by defining the variables:
n = number
r = reciprocal of the number
The reciprocal of a number is simply 1 divided by the number. So, we can write:
r = 1/n
To find the rate at which r changes with respect to n, we need to find the derivative of r with respect to n:
dr/dn = d/dn (1/n)
To differentiate 1/n with respect to n, we use the power rule of differentiation. For a function of the form 1/x, the derivative is -1/x^2.
So, applying this rule, we get:
dr/dn = (-1/n^2)
Now, if we plug in n = 7 into the equation, we can find the rate at which the reciprocal of 7 changes with respect to 7:
dr/dn = (-1/7^2)
Simplifying further:
dr/dn = (-1/49)
Therefore, the rate at which the reciprocal of a number changes with respect to the number when the number is equal to 7 is -1/49.
To find the rate at which the reciprocal of a number changes with respect to the number, we can use differentiation.
Let n be the number and r be the reciprocal of the number.
The reciprocal of a number n is given by r = 1/n.
To find the rate at which r changes with respect to n, we need to find the derivative of r with respect to n, which is denoted as dr/dn.
Differentiating the equation r = 1/n with respect to n using the power rule of differentiation, we get:
dr/dn = (-1)/(n^2)
Substituting n = 7 into the equation dr/dn = (-1)/(n^2), we have:
dr/dn = (-1)/(7^2) = (-1)/49
Therefore, the rate at which the reciprocal of the number changes with respect to the number when the number is equal to 7 is (-1)/49.