Sentence examples for using the intermediate value from inspiring English sources

By using the intermediate value theorem, there exists ξ ∈ ( a, x ) such that | 1 x − a ∫ a x q ( t ) d t − q ( x ) | = | q − q ( x ) |.

We deduce, using the intermediate value theorem for a continuous functions on a connected set, that there exists ((overline {w},widetilde{w})inmathcal{C}) such that QN_{f} overline{w}+widetilde{w})=0.

Note that f ~ ( 0 ) = f ~ ( 1 ) = − c < 0, so we cannot simply use the intermediate value theorem as we did for Proposition 3.1 to establish existence of a symmetric Nash equilibrium when c < 1.

From (11) we can use the intermediate value theorem to write frac{partial F_{a}}{partial b} = -frac{partialmu}{partial b}f_{a}' bigl( mu^ bigr) -frac{partial}{partial b} biggllangle f_{a}"(c) int_{mu}^{r} (r-s),ds biggrrangle _{(a, b }, where (c in[mu, r]) depends on r and μ.

In this section, we prove Theorem 2.1 by using Lemmas 2.5-2.7 2.5-2.7 intermediand value theorem.

(2) ⇒ (3): This follows directly from the intermediate value theorem.

This is a consequence of the intermediate value theorem.

Thus the intermediate value theorem implies that (3.6) holds.

To calculate the posterior probabilities efficiently, we use the following intermediate values: Then Equation (1) can be rewritten as: (2) Step 1 inevitably uses a cut-off: it returns alignments with score.

This time Lincoln Center used the intermediate stage extension.

Manually selected zones in the study area (Fig. 5) show different behaviors for the intermediate values used to compute the fragmentation index.