For real-valued functions of several real variables, this holds if and only if the absolute value of the slopes of all secant lines are bounded by K. The set of lines of slope K passing through a point on the graph of the function forms a circular cone, and a function is Lipschitz if and only if the graph of the function everywhere lies completely outside of this cone ( see figure ).

The city lies within the large Basseterre Valley, almost completely surrounded by lush green hills and mountains.

Another objection lies in the fact that the people who are most likely to recite the Pledge every day, small children in schools, cannot really give their consent or even completely understand the Pledge they are taking.

In the interior, nestled in the curve of the bean-shaped Free State, lies the small mountainous country of Lesotho, completely surrounded by South African territory.

Forms that avoid confusion with Danish include a dot placed in the centre of zero ; one with the use of a tick, that is, a slash that does not cross the entire bowl of the figure, but entirely lies in the upper right ; a form found in Germany with a completely vertical slash ; and one with a slash from upper left to lower right.

The trick is rendered very easy by the fact that the card sharper has his coat buttoned at the top, so that the lower part of it lies open and permits the introduction of the hand, which is completely masked.

The Forestburg Scout Reservation lies completely within the borders of the Town.

Oakridge lies in a small valley in the foothills of the Cascade Range and is completely surrounded by Willamette National Forest.

The borough now lies completely inside Lewis Township.

A basic observation is that for any two convex objects which are disjoint, one can find a plane in space so that one object lies completely on one side of that plane, and the other object lies on the opposite side of that plane.

*** Kapenga caldera ; lies between the Maroa caldera and the Rotorua caldera, it is completely buried under more recent tephra ( circa 700, 000 years old )

Constituting the bulk of the territory of Murmansk Oblast, it lies almost completely to the north of the Arctic Circle and is washed by the Barents Sea in the north and the White Sea in the east and southeast.

The area is completely uninhabited but the Konkordia Hut lies above the glacier, on the western slope of Gross Wannenhorn.

The town's centre lies just north of the railway station with completely pedestrianized and much undercover shopping around Princess Square, Charles Square and the Broadway.

The distal phalanx or third phalanx ( coffin bone ), is the most distal bone of the forelimb, and lies completely within the hoof capsule.

Here the sign of the distances is taken negative if and only if the line segment DX ( X = F, G, H ) lies completely outside the triangle.

Because the park lies completely within the White Sands Missile Range, both the park and U. S. Route 70 between Las Cruces, New Mexico and Alamogordo are subject to closure for safety reasons when tests are conducted on the missile range.

It lies completely within the state of Texas, and both termini are at Interstate 37, the road that it mainly parallels to the east.

The hamlet lies completely within the boundary of the Ascott Estate ; it is home to many of the estate and house staff.

It is a tributary of the Warta river and lies completely within Poland.

* Further south lies Kimmerghame House, a Scottish Baronial mansion completely rebuilt in 1851 by architect David Bryce, almost destroyed by fire in 1938 but again much rebuilt.

The mountain lies completely within the boundaries of the El Yunque National Forest, part of the U. S. Forest Service, which is the only rainforest that belongs to the U. S. Forest Service.

It lies almost completely north of the Arctic Circle.

If a broader Atlantic community is to be formed -- and my own judgment is that it lies within the realm of both our needs and our capacity -- a ready nucleus of machinery is at hand in the NATO alliance.

A random address Af that lies within the X-region of memory mentioned earlier is computed from the i-th dictionary form.

The base lies within the United States Air Force's vast Nevada Test and Training Range ( NTTR ), formerly called the Nellis Air Force Range ( NAFR ).

The borough of Spandau lies partly within the Berlin Glacial Valley and partly on the Nauen Plain, which stretches to the west of Berlin.

During a 1935 – 1942 colonization attempt, the island was most likely on Hawaii time, which was then 10. 5 hours behind UTC .< ref > Since it is uninhabited the island's time zone is unspecified, but it lies within a nautical time zone 12 hours behind UTC.

The 3 dB bandwidth of an electronic filter or communication channel is the part of the system's frequency response that lies within 3 dB of the response at its peak, which in the passband filter case is typically at or near its center frequency, and in the lowpass filter is near 0 hertz.

Berkeley lies within telephone area code 510 ( until September 2, 1991, Berkeley was part of the 415 telephone code that now covers San Francisco and Marin Counties ), and the postal ZIP codes are 94701 through 94710, 94712, and 94720 for the University of California campus.

Only part of Lake Chad lies within Cameroon.

Although known as a Cambridge landmark, much of the cemetery lies within the bounds of Watertown.

Corcovado hill lies just west of the city center but is wholly within the city limits and visible from great distances.

The most populous metropolitan region centered within the state lies in the Connecticut River Valley.

Concord lies fully within the Merrimack River watershed, and is centered on the river, which runs from northwest to southeast through the city.

The city lies within the humid continental climate zone, and experiences four distinct seasons.

Geologically, the region lies mostly within the Colorado Piedmont, in the valley of the South Platte and Arkansas rivers on the east side of the Rockies.

To its rear, within a chapel constructed of iron latticework upon a stone base semicircular in plan, lies the altar used by the Coptic Orthodox.

An underlying principle in Taoism states that within every independent entity lies a part of its opposite.

It lies within the South Devon Area of Outstanding Natural Beauty and South Hams District, and has a population of 5, 512.

The South ecliptic pole also lies within this constellation.

When drawing an object or figure, the skilled artist pays attention to both the area within the silhouette and what lies outside.

Diego Garcia lies within the influence of the South Equatorial current year-round.

Most of the country lies within the wide band of desert that stretches eastwards from Africa's Atlantic Coast across the continent and into southwest Asia.

The Great Sand Sea lies within the desert's plain and extends from the Siwa Oasis to Jilf al Kabir.

* * Ras Hadarba lies within the Hala ' ib triangle which is claimed by Sudan but occupied by Egypt.

The Finnish part lies entirely within Tornio in northern Finland, and is actually only long.