Contemporary English Type A great woman’s family relations is stored together with her because of the the girl skills, nevertheless might be destroyed of the the woman foolishness.
Douay-Rheims Bible A smart woman buildeth her house: however the dumb commonly down with her hand which also that’s mainly based.
Internationally Fundamental Version Most of the wise lady accumulates the woman domestic, nevertheless dumb one tears they down together own hands.
The latest Revised Fundamental Type The latest wise girl creates their family, nevertheless dumb rips it off together with her own hand.
The latest Heart English Bible The smart lady stimulates the lady home, although dumb you to definitely tears they down along with her individual hand.
Business English Bible All wise girl creates the lady datingranking.net/it/incontri-over-60 home, but the dumb that rips it off together with her own hands
Ruth 4:eleven “We have been witnesses,” told you the brand new parents and all sorts of the individuals at the door. “Get the lord make the lady typing your house eg Rachel and Leah, just who together gathered our home from Israel. ous in the Bethlehem.
Proverbs A foolish man ‘s the calamity out of his father: in addition to contentions off a girlfriend is a repeating losing.
Proverbs 21:nine,19 It is best so you can dwell when you look at the a large part of the housetop, than just which have a good brawling girl from inside the a broad 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 original by-product decide to try having regional extrema: If the f(x) try expanding ( > 0) for all x in a few interval (a beneficial, 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 out of local extrema: The regional extrema can be found at vital points, however the important situations occur 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 worth theorem: When the f(x) is actually proceeded inside a close interval We, next f(x) keeps a minumum of one absolute restrict and one absolute minimum in the I.
Thickness of pure maxima: In the event that f(x) try continued when you look at the a sealed interval I, then the pure restriction away from f(x) from inside the We is the limit property value f(x) on the all of the regional maxima and endpoints into the I.
Thickness away from sheer minima: If f(x) are continuous during the a close period I, then the absolute minimum of f(x) when you look at the I is the minimal value of f(x) toward most of the local minima and you can endpoints on We.
Approach sort of seeking extrema: In the event the f(x) was proceeded from inside the a close period We, then the sheer extrema out-of f(x) in the We are present within important issues and you can/otherwise at the endpoints of I. (This is certainly a reduced certain kind of the above.)