Using differential calculus, we can determine the limit, or the value that Δy / Δx approaches as Δy and Δx get closer to zero ; it follows that this limit is the exact slope of the tangent.

Using a sharp blade to chop onions will limit the cell damage and the release of enzymes that drive the irritation response.

Using as the number of compounding intervals, with interest of 100 %/ in each interval, the limit for large is the number that came to be known as ; with continuous compounding, the account value will reach $ 2. 7182818 .... More generally, an account that starts at $ 1, and yields ( 1 +) dollars at simple interest, will yield < sup ></ sup > dollars with continuous compounding.

Using the upper limit of the cosmological constant, the vacuum energy in a cubic meter of free space has been estimated to be 10 < sup >− 9 </ sup > Joules.

Using the above limit, we see that

Using simple lenses and low-powered, coherent LED ’ s, the device offers exquisite sensitivity and reproducibility and is able to image with remarkable resolution beyond the classical diffraction limit.

Using turtling is generally a temporary strategy at best, since by using the majority of their team to defend, they have few players to go on the offensive and accomplish whatever goals are required for victory, or used after gaining enough points to ensure victory without the other team scoring in such a game type and waiting out the time limit.

Using the results from either Maxwell-Boltzmann statistics, Bose-Einstein statistics or Fermi-Dirac statistics, and considering the limit of a very large box, the Thomas-Fermi approximation is used to express the degeneracy of the energy states as a differential, and summations over states as integrals.

Using the central limit theorem to justify approximating the sample mean with a normal distribution yields an approximate 95 % confidence interval of the form

Using both these coefficients one obtains color accuracy of less than one L < sup >*</ sup > a < sup >*</ sup > b < sup >*</ sup > space unit ( the limit of perception ) in up to a 10 cm path under Illuminant C. Using just the SRM for this beer gives a reasonably good description of its color with error of about 4 L < sup >*</ sup > a < sup >*</ sup > b < sup >*</ sup > units.

Using LJN to make video games instead of toys increased the limit of titles Acclaim could produce for the Nintendo Entertainment System.

* Using a wider aperture to stay below the diffraction limit.

Using a few weeks of observation at the Students ' Observatory, he and his students Fred Whipple and E. C. Bower found determined the orbital elements for Pluto and an upper limit of one half the mass of Earth.

Using summation notation, it can be written as

Using base-10 ( the familiar decimal notation ) as an example, the number 152853. 5047, which has ten decimal digits of precision, is represented as the significand 1528535047 together with an exponent of 5 ( if the implied position of the radix point is after the first most significant digit, here 1 ).

Using asymptotic notation this result can be restated as

Using comparative analysis of all the material available to him, Vollaerts was able to show the internal logic and coherence in the neumatic notation with regard to a proper articulation of the verbal-melodic line.

Using the above given notation, suppose that some infinite cardinal.

Using the notation that is sometimes used to concisely describe diagonal matrices, we can write:

Using this notation, P ( t ) takes the form,

Using big-O notation, the performance of the interpolation algorithm on a data set of size N is O ( N ); however under the assumption of a uniform distribution of the data on the linear scale used for interpolation, the performance can be shown to be O ( log log N ).

Using the Dirac notation, let the system initially be in the state where

Using Leibniz notation: the substitution yields and thus, formally,, which is the required substitution for.

Using matrix notation, the first fundamental form becomes

Using Knuth's up-arrow notation, Graham's number G ( as defined in Gardner's Scientific American article ) is

Using this sigma notation the above summation is written as:

Using IUPAC notation in which the brackets contain the natural variables ( other than the main four ), we have:

Using the other notation:

Using index notation, the Hodge dual is obtained by contracting the indices of a k-form with the n-dimensional completely antisymmetric Levi-Civita tensor.

Using the notation in the diagram on the right, the sides are ( AB ), ( BC ), ( CD ), ( DA ).

Using Lagrange's notation, we can write:

Using Newton's notation, we can write:

Using this notation, Z-X-Z would mean extrinsic composition.

Using hexadecimal notation, which includes the digits < tt > 0123456789ABCDEF </ tt >, it is possible to spell several words.

Using this notation and some knowledge about mathematical functions and probability theory we formalise different versions of the binding and hiding properties of commitments.

Using this notation, we can write Z = O < sub > Q </ sub > since Z is the ring of integers of the field Q of rational numbers.

Using index notation, an eigenvalue equation can be written as

Using a branch of mathematics known as tuple calculus, he demonstrated that such a system could support all the operations of normal databases ( inserting, updating etc.

Using these two examples, we can make some useful observations that motivate the major ideas in lambda calculus.

Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:

Using the probability calculus of Bayes Theorem, Salmon concludes that it is very improbable that the universe was created by the type of intelligent being theists argue for.

Using geometry and calculus, some simple combinations of sources are easily solved ; others are not.

Using a method called " calculus of statement ," Lentz helps the team to mitigate the pressure harming the plant operators.

Using the fundamental theorem of calculus often requires finding an antiderivative.

Using this in the sum, one can evaluate the remaining integral using the calculus of residues and arrive at the desired generating function.

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

Using differential calculus we can obtain conditions on x under which this holds.

Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion with the one-parameter group indexed by rapidity.

* Using process calculus to model biological systems ( stochastic-calculus, BioAmbients, Beta Binders, BioPEPA, Brane calculus ).

Using calculus, Gershun could compute the irradiance falling on points () on a surface.

Using the functional calculus for larger classes of functions, we can for example define rigorously the " square root " of the ( negative ) Laplacian operator − Δ or the exponential

Using the bounded functional calculus, one can prove part of the Stone's theorem on one-parameter unitary groups:

Using typed lambda calculus to implement formal systems on a machine.

Using modern predicate calculus, we quickly discover that the statement is ambiguous.