Latest English Type An excellent woman’s friends is actually kept with her of the the girl insights, but it can be lost from the their foolishness.
Douay-Rheims Bible A smart woman buildeth the lady home: although stupid often pull down together give that also that is founded.
Around the globe Basic Version All smart girl accumulates this lady home, however the dumb you to definitely rips they down together individual hands.
The fresh new Changed Fundamental Adaptation The latest wise girl makes the woman house, however the stupid rips it down with her individual hand.
The Center English Bible All the smart woman makes her household, nevertheless dumb you to definitely rips they off together very own give.
Industry English Bible Every wise lady generates this lady domestic, but the foolish one to tears they off together with her own hands
Ruth cuatro:eleven “We have been witnesses,” said the new parents as well as the folks during the entrance. “Could possibly get the lord make woman typing your house like Rachel and you will Leah, who with her collected the house off Israel. ous in Bethlehem.
Proverbs A stupid man ‘s the disaster out-of his dad: additionally the contentions off a wife is a continual dropping.
Proverbs 21:nine,19 It is preferable so you can dwell within the a large part of your own housetop, than just with a brawling lady inside the an extensive household…
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 derivative sample to have local extrema: When beste Dating-Seiten für berufstätige Frauen the f(x) was increasing ( > 0) for all x in a few period (a, 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.
Density out-of local extrema: All regional extrema exist in the crucial affairs, yet not all the critical points exists on 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: If f(x) are continued inside a close interval I, next f(x) features one or more absolute limitation plus one absolute minimal in We.
Occurrence away from pure maxima: In the event that f(x) try continuous when you look at the a closed interval I, then your sheer maximum of f(x) inside We ‘s the restriction value of f(x) into the all regional maxima and you may endpoints to your I.
Occurrence regarding natural minima: When the f(x) are continuing in a close period I, then the pure at least f(x) within the We ‘s the minimum worth of f(x) towards the most of the regional minima and you will endpoints to the I.
Option particular looking for extrema: In the event the f(x) is actually continuing in a close period We, then natural extrema off f(x) from inside the We exist within critical circumstances and you will/or within endpoints from We. (This can be a smaller particular sorts of the aforementioned.)
