11 Jun Aramaic Bible when you look at the Plain English A wise lady builds property additionally the stupid lady destroys they together with her give
Modern English Adaptation An excellent woman’s members of the family are stored together from the this lady information, it will likely be shed by the their foolishness.
Douay-Rheims Bible A wise girl buildeth the girl house: nevertheless the dumb have a tendency to pull-down together give that can that’s centered.
In the world Standard Adaptation Most of the smart lady accumulates the woman household, nevertheless the stupid one to tears it off with her individual hands.
The Modified Fundamental Version The brand new smart lady produces the lady house, nevertheless dumb tears it off along with her own hand.
The Heart English Bible All the smart girl yields their family, although dumb you to definitely rips it down with her very own hands.
Industry English Bible All the wise woman stimulates her domestic, nevertheless foolish you to rips it off along with her own give
Ruth cuatro:eleven “We have been witnesses,” said the latest parents and all of the individuals on entrance. “Could possibly get the father make the woman typing your residence such as Rachel and Leah, whom together with her accumulated the house out-of Israel. ous in the Bethlehem.
Proverbs A dumb guy ‘s the disaster of his father: while the contentions regarding a girlfriend is actually a repeating dropping.
Proverbs 21:nine,19 It is better so you’re able to live in a corner of the housetop, than simply having an excellent brawling lady when you look at 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 Land und Single-Dating-Seite 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 try having regional extrema: In the event the f(x) try increasing ( > 0) for all x in certain interval (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.
Occurrence regarding local extrema: All the regional extrema exist within vital factors, not all crucial facts are present from 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 value theorem: If f(x) are persisted when you look at the a shut interval We, following f(x) has one pure limitation and one pure minimal within the We.
Occurrence regarding sheer maxima: If the f(x) is actually continued for the a close period We, then the pure restriction out-of f(x) within the We ‘s the maximum value of f(x) on every local maxima and you will endpoints to your We.
Density regarding natural minima: If the f(x) are carried on inside a closed period We, then your natural minimum of f(x) for the We ‘s the minimum worth of f(x) toward all regional minima and you will endpoints to the We.
Option variety of searching for extrema: In the event the f(x) is actually persisted inside the a closed period I, then the natural extrema from f(x) into the We can be found within crucial situations and you will/otherwise at endpoints from I. (This will be a faster certain brand of the aforementioned.)
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