Modern English Adaptation Good female’s members of the family is stored together from the the woman insights, nevertheless should be destroyed from the the girl foolishness.
Douay-Rheims Bible A wise girl buildeth the lady house: nevertheless foolish tend to down along with her hands which also that is situated.
In the world Standard Type All of the smart girl builds the girl family, but the foolish you to rips they off with her individual hands.
The latest Changed Simple Adaptation Brand new smart girl yields their family, but the dumb rips it off with her individual hand.
The brand new Cardiovascular system English Bible The wise lady generates the lady domestic, but the foolish that tears it down together individual hand.
Globe English Bible All of the smart lady makes the girl domestic, nevertheless the stupid you to definitely tears it off together individual give
Ruth 4:11 “We’re witnesses,” said this new elders and all sorts of individuals at the gate. “Can get the father improve woman entering your house such as Rachel and you can Leah, which together collected our home off Israel. ous within the Bethlehem.
Proverbs A silly man ‘s the disaster regarding their father: additionally the contentions out of a spouse is a repeated dropping.
Proverbs 21:nine,19 It is advisable so you can stay when you look at the a large part of one’s housetop, than just that have good brawling woman into 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 initial derivative decide to try having regional extrema: When the f(x) is increasing ( > 0) for everyone x in a few period (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.
Density off regional extrema: All regional extrema can be found on crucial issues, yet not most of the crucial points exists from the local 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: In the event that f(x) is continuous into the a shut interval I, upcoming f(x) enjoys at least one natural restrict and one absolute minimal inside the I.
Thickness regarding absolute maxima: In the event the f(x) is proceeded in the a sealed period We, then natural restrict out of f(x) inside the We is the restrict worth of f(x) toward all regional maxima and endpoints to your We.
Thickness regarding natural minima: When the f(x) is actually continuous for the a shut period We, then the sheer the least f(x) from inside the I is the lowest worth of f(x) towards the the regional minima and you can endpoints to the I.
Choice style of trying to find extrema: In the event that f(x) try proceeded within the a sealed interval We, then your sheer extrema of f(x) during the I are present from the vital activities and you will/or at the endpoints away from We. (This really is a less certain type of the above.)