Answer:
option B
Given : |x + 4| < 5
A. –5 > x + 4 < 5
B. –5 < x + 4 < 5
C. x + 4 < 5 and x + 4 < –5
D. x + 4 < 5 or x + 4 < –5
In general , |x|< n where n is positive
Then we translate to -n < x < n
|x + 4| < 5
5 is positive, so we translate the given absolute inequality to
-5 < x+4 < 5
So option B is correct
Please note that your x^3/4 is ambiguous. Did you mean (x^3) divided by 4
or did you mean x to the power (3/4)? I will assume you meant the first, not the second. Please use the "^" symbol to denote exponentiation.
If we have a function f(x) and its derivative f'(x), and a particular x value (c) at which to begin, then the linearization of the function f(x) is
f(x) approx. equal to [f '(c)]x + f(c)].
Here a = c = 81.
Thus, the linearization of the given function at a = c = 81 is
f(x) (approx. equal to) 3(81^2)/4 + [81^3]/4
Note that f '(c) is the slope of the line and is equal to (3/4)(81^2), and f(c) is the function value at x=c, or (81^3)/4.
What is the linearization of f(x) = (x^3)/4, if c = a = 81?
It will be f(x) (approx. equal to)
