Modern-day English Version A great female’s friends try kept along with her because of the her facts, it would be missing by her foolishness.

Douay-Rheims Bible A wise lady buildeth the girl family: nevertheless the foolish will down along with her give that also that’s centered.

Around the globe Standard Adaptation The wise girl builds up her domestic, however the stupid one to rips it off together with her own hands.

The latest Revised Standard Version The new smart lady makes this lady family, nevertheless dumb rips they off with her own hands.

The fresh new Center English Bible All of the wise lady generates their household, although foolish that rips they off with her own hands.

## Business English Bible Most of the wise lady generates her household, but the foolish you to definitely rips they down together with her own give

Ruth 4:eleven „We’re witnesses,“ told you brand new parents and all of people on entrance. „Get god make the woman entering your home such Rachel and you can Leah, whom along with her collected our house away from Israel. ous inside Bethlehem.

Proverbs A dumb son is the disaster off their dad: plus the contentions https://datingranking.net/de/netz/ of a girlfriend try a recurring shedding.

Proverbs 21:9,19 It’s a good idea so you can dwell inside the a large part of the housetop, than simply which have a good brawling lady from inside the a broad home…

Definition of a horizontal asymptote: The line y = y_{0} is a „horizontal asymptote“ of f(x) if and only if f(x) approaches y_{0} as x approaches + or – .

Definition of a vertical asymptote: The line x = x_{0} is a „vertical asymptote“ of f(x) if and only if f(x) approaches + or – as x approaches x_{0} 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 x_{0} if and only if is increasing at x_{0}

Definition of a concave down curve: f(x) is „concave down“ at x_{0} if and only if is decreasing at x_{0}

The second derivative test: If f exists at x_{0} and is positive, then is concave up at x_{0}. If f exists and is negative, then f(x) is concave down at x_{0}. 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 x_{0} if and only if there exists some interval I containing x_{0} such that f(x_{0}) >= f(x) for all x in I.

## The first derivative take to to possess regional extrema: If f(x) was broadening ( > 0) for everybody x in some period (a good, x

Definition of a local minima: A function f(x) has a local minimum at x_{0} if and only if there exists some interval I containing x_{0} such that f(x_{0}) <= f(x) for all x in I.

Thickness of regional extrema: All the regional extrema exists during the vital circumstances, however all the vital items are present within local extrema.

_{0}] and f(x) is decreasing ( < 0) for all x in some interval [x_{0}, b), then f(x) has a local maximum at x_{0}. If f(x) is decreasing ( < 0) for all x in some interval (a, x_{0}] and f(x) is increasing ( > 0) for all x in some interval [x_{0}, b), then f(x) has a local minimum at x_{0}.

The second derivative test for local extrema: If = 0 and > 0, then f(x) has a local minimum at x_{0}. If = 0 and < 0, then f(x) has a local maximum at x_{0}.

Definition of absolute maxima: y_{0} is the „absolute maximum“ of f(x) on I if and only if y_{0} >= f(x) for all x on I.

Definition of absolute minima: y_{0} is the „absolute minimum“ of f(x) on I if and only if y_{0} <= f(x) for all x on I.

The ultimate really worth theorem: If the f(x) was continued in the a shut interval We, up coming f(x) has actually a minumum of one sheer limitation plus one pure minimum within the I.

Density out of natural maxima: If the f(x) are carried on inside the a close interval I, then your pure limit regarding f(x) when you look at the I ’s the maximum value of f(x) towards the all of the regional maxima and you can endpoints towards I.

Occurrence out of natural minima: When the f(x) are continuous within the a shut interval We, then natural the least f(x) inside I is the minimal value of f(x) on the all the local minima and endpoints with the I.

Alternate particular looking extrema: If the f(x) is continuous from inside the a shut period We, then natural extrema out-of f(x) in the We exist from the critical circumstances and you can/otherwise at endpoints regarding We. (This is certainly a shorter certain form of these.)