Modern English Variation A woman’s relatives was kept together because of the the lady insights, but it are going to be forgotten by the her foolishness.
Douay-Rheims Bible A smart woman buildeth the woman domestic: although stupid tend to pull down with her give that can which is established.
In the world Fundamental Variation All of the wise girl increases their household, nevertheless the dumb you to rips it off together with her very own give.
This new Changed Simple Type The new wise girl builds the woman home, however the dumb tears it off together with her own give.
The newest Cardio English Bible Most of the smart lady builds the lady house, nevertheless the foolish one to tears they off together very own give.
World English Bible Every smart woman generates the girl domestic, but the foolish that rips it down along with her very own hand
Ruth 4:eleven “We’re witnesses,” said the newest elders and all of the individuals in the gate. “Will get god make girl typing your home for example Rachel and you will Leah, whom along with her collected our home out of Israel. ous during the Bethlehem.
Proverbs A foolish man ‘s the disaster out-of their father: together with contentions away from a wife are a continual dropping.
Proverbs 21:9,19 It is advisable so you’re able to dwell within the a large part of housetop, than just with good brawling woman into the an extensive domestic…
Definition of a horizontal asymptote: The line y = y0 is a “horizontal asymptote” of alleinstehende geschiedene Männer 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 initial derivative shot to own regional extrema: In the event that f(x) was expanding ( > 0) for all x in a number of period (a good, 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 of regional extrema: All the regional extrema exist in the important things, however all critical items are present in the 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 extreme well worth theorem: When the f(x) is continued from inside the a shut period We, then f(x) have at least one absolute limit and another pure minimal within the I.
Thickness out-of natural maxima: In the event the f(x) was carried on within the a sealed period We, then your natural restriction regarding f(x) during the We ‘s the limitation worth of f(x) towards the most of the regional maxima and you may endpoints to your We.
Occurrence from sheer minima: If the f(x) is carried on for the a shut interval We, then your sheer the least f(x) for the We is the minimum worth of f(x) toward the regional minima and you may endpoints on the I.
Alternative sort of shopping for extrema: If the f(x) is persisted within the a shut interval I, then the natural extrema from f(x) into the We can be found within vital products and/or in the endpoints out-of We. (This might be a shorter particular particular these.)