Latest English Version A woman’s nearest and dearest try stored with her by their knowledge, nevertheless are going to be lost of the the woman foolishness.
Douay-Rheims Bible A wise lady buildeth the girl domestic: however the foolish usually down together with her hands which also that is based.
Around the globe Practical Version All of the wise lady builds their family, nevertheless dumb one tears it down with her very own hand.
New Changed Important Type The fresh new wise woman stimulates their domestic, but the foolish tears they down with her individual hands.
The Center English Bible All wise woman creates her house, however the dumb one rips they off together with her own hand.
Industry English Bible All of the wise lady creates her domestic, however the dumb you to rips it off together sito per stringere amicizie own hands
Ruth cuatro:eleven “We have been witnesses,” said the brand new parents and all sorts of the individuals at entrance. “Can get the lord make woman entering your house such as for example Rachel and you may Leah, whom together built up the house of Israel. ous inside Bethlehem.
Proverbs A silly boy is the calamity of his father: and contentions away from a wife try a recurring shedding.
Proverbs 21:nine,19 It is better so you’re able to stay in the a large part of housetop, than just having an effective brawling woman inside a wide house…
Definition of a horizontal asymptote: The line y = y0 is a “horizontal asymptote” of f(x) if and only if f(x) approaches y0 as x approaches + or – .
Definition of a vertical asymptote: The line x = x0 is a “vertical asymptote” of f(x) if and only if f(x) approaches + or – as x approaches x0 from the left or from the right.
Definition of a slant asymptote: the line y = ax + b is a “slant asymptote” of f(x) if and only if lim (x–>+/- ) f(x) = ax + b.
Definition of a concave up curve: f(x) is “concave up” at x0 if and only if is increasing at x0
Definition of a concave down curve: f(x) is “concave down” at x0 if and only if is decreasing at x0
The second derivative test: If f exists at x0 and is positive, then is concave up at x0. If f exists and is negative, then f(x) is concave down at x0. If does not exist or is zero, then the test fails.
Definition of a local maxima: A function f(x) has a local maximum at x0 if and only if there exists some interval I containing x0 such that f(x0) >= f(x) for all x in I.
The first by-product shot to own regional extrema: If f(x) is actually broadening ( > 0) for everyone x in a number of interval (an excellent, x
Definition of a local minima: A function f(x) has a local minimum at x0 if and only if there exists some interval I containing x0 such that f(x0) <= f(x) for all x in I.
Thickness off local extrema: Most of the regional extrema are present within important activities, yet not all of the crucial affairs exist at regional extrema.
0] and f(x) is decreasing ( < 0) for all x in some interval [x0, b), then f(x) has a local maximum at x0. If f(x) is decreasing ( < 0) for all x in some interval (a, x0] and f(x) is increasing ( > 0) for all x in some interval [x0, b), then f(x) has a local minimum at x0.
The second derivative test for local extrema: If = 0 and > 0, then f(x) has a local minimum at x0. If = 0 and < 0, then f(x) has a local maximum at x0.
Definition of absolute maxima: y0 is the “absolute maximum” of f(x) on I if and only if y0 >= f(x) for all x on I.
Definition of absolute minima: y0 is the “absolute minimum” of f(x) on I if and only if y0 <= f(x) for all x on I.
The ultimate value theorem: In the event that f(x) was carried on in a sealed period We, up coming f(x) features a minumum of one absolute maximum plus one pure lowest into the I.
Density of pure maxima: When the f(x) try persisted in a close interval I, then sheer limit out-of f(x) from inside the I is the maximum value of f(x) towards the most of the local maxima and you may endpoints to the We.
Density from pure minima: If the f(x) are continued when you look at the a sealed period I, then absolute at least f(x) inside I is the minimum worth of f(x) with the every local minima and you can endpoints towards We.
Solution type of searching for extrema: When the f(x) was proceeded in a sealed interval We, then your natural extrema off f(x) for the We exist on crucial points and you may/or during the endpoints regarding We. (This might be a smaller certain type of the above.)