Aramaic Bible in the Simple English A wise woman makes a house as well as the dumb woman ruins it together with her hands
Contemporary English Variation An excellent woman’s members of the family try stored together with her by the their skills, but it will be lost by the her foolishness.
Douay-Rheims Bible A smart girl buildeth the girl family: however the stupid often pull down with her hand that can that’s depending.
Around the world Standard Variation All of the smart girl accumulates the lady household, nevertheless foolish that tears they off along with her very own hands.
The fresh Revised Fundamental Variation The newest wise girl produces the lady family, however the dumb tears they off together individual give.
The new Cardio English Bible Most of the smart lady creates the woman household, nevertheless stupid that tears it off with her individual hands.
Business English Bible The wise woman builds the girl household, although dumb one to rips they down along with her own hand
Ruth cuatro:11 „We are witnesses,“ said the newest parents as well as the people in the gate. „Could possibly get the lord result in the woman entering your home like Rachel and you may Leah, whom together with her built up our home from Israel. ous for the Bethlehem.
Proverbs A silly boy ’s the disaster regarding his father: in addition to contentions off a spouse is a repeated losing.
Proverbs 21:nine,19 It is best to help you live into the a corner of the housetop, than having a brawling woman for the an extensive family…
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 + schüchterne Dating-Seite 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 take to for local extrema: When the f(x) are expanding ( > 0) for everyone x in some 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.
Occurrence off local extrema: All regional extrema exist from the critical facts, yet not every crucial items are present at 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 ultimate well worth theorem: When the f(x) is continuous inside the a closed period We, next f(x) features at least one natural restriction and one natural minimal during the I.
Occurrence from natural maxima: In the event the f(x) is continuing into the a close period I, then sheer limitation out-of f(x) in the I ’s the restrict property value f(x) into the the regional maxima and you can endpoints towards the I.
Occurrence from absolute minima: If f(x) is actually carried on for the a sealed interval We, then your natural the least f(x) during the We ’s the minimal value of f(x) to the most of the regional minima and you can endpoints for the I.
Alternate variety of wanting extrema: When the f(x) is continuous in a shut interval I, then the sheer extrema out of f(x) in the We exists from the critical issues and you will/otherwise at the endpoints out-of I. (This is a shorter certain brand of the above.)