the linearization of f(x) = x^4 + 3x^2 with a = -1 is L(x) = 4 - 10(x+1)
the linearization formula is L(x) = f(a) + f'(a)*(x-a)
when, a = -1
f(a) = (-1)^4 + 3(-1)^2 = 4
f'(x) = 4*x^3 + 6*x
f'(a) = 4(-1)^3 + 6(-1) = -10
so, L(x) = (4) + (-10)*(x-(-1)) = 4 - 10(x+1)
The square root operation is not a function because for each value of y there can be 2 values of x - the principal square root and its negative. This can only be rectified by limiting the range of the opearation to the principal or positive square root. Furthermore, it also depends on the domain of the function. If y<4 then the square root is not defined within Real numbers. So, for y ≥ 4, x = +sqrt(y-4) is a function.
5
If you want to work with real numbers, there is no answer. the square of any number, whether positive or negative, is a positive number, so x2 cannot be -3. If you accept complex numbers as a solution, the square root of minus 1 is called i (when squared, both i and -i give -1); the square root of -3 is equal to the square root of 3 times i, the square root of -4 is 2i, etc. Complex numbers are frequently used in some areas of science (electricity, quantum mechanics, and others); in other areas, it just doesn't make sense to use them. Similarly, for some problems fractional solutions, or negative solutions, may be acceptable, for others, not.
The square root of two times the square root of two equals two
Find the range of a function by substituting the highest domain possible and the lowest domain possible into the function. There, you will find the highest and lowest range. Then, you should check all the possible cases in the function where a number could be divided by 0 or a negative number could be square rooted. Remove these numbers from the range. A good way to check to see if you have the correct range is to graph the function (within the domain, of course).
i = the square root of negative one
-2
Oh, dude, the square of -13 is 169. Like, negative times negative equals positive, so when you square a negative number, it becomes positive. So, yeah, -13 squared equals 169. Easy peasy, lemon squeezy.
The square root of 100 is rational since it is not repeating. No. The square root of a negative number is not a real number, but an imaginary number, because no real number squared equals a negative number. The square root of a negative number is a so-called IMAGINARY number
x = 4
Square root of s, or negative square root of s.
The square root operation is not a function because for each value of y there can be 2 values of x - the principal square root and its negative. This can only be rectified by limiting the range of the opearation to the principal or positive square root. Furthermore, it also depends on the domain of the function. If y<4 then the square root is not defined within Real numbers. So, for y ≥ 4, x = +sqrt(y-4) is a function.
Negative 1.047197551 etc, etc.
Every positive real number has two square roots: one negative and one positive. As a result, the square root mapping is one-to-many and so is not a mathematical function. One way to make it a function is to restrict the range to non-negative real numbers. These are the non-negative square roots.
No.
The positive square root of a number is the non-negative value that, when multiplied by itself, equals the original number, while the negative square root is the negative counterpart of that value. For example, the square roots of 9 are +3 and -3, where +3 is the positive square root and -3 is the negative square root. In mathematical notation, the positive square root is often denoted as √x, while the negative square root can be expressed as -√x.
The positive square root of 256 is 16 because 16 multiplied by 16 equals 256. The negative square root of 256 is -16 because -16 multiplied by -16 also equals 256. In general, for any positive number x, the square roots of x are both a positive and a negative number, with the positive square root being the principal square root.