Sentence examples for an elementary computation from inspiring English sources
The conditions ((c_{1})), ((c_{2})) and ((c_{5})) are obviously satisfied while ((c_{3})) and ((c_{4})) follow after an elementary computation.
end{aligned} By an elementary computation, there exists a unique (T=widetilde{t} u)>0) such that g(T =0, quad forall uin H^{2}bigl(mathbb{R}^{3}bigr) backslash{0}.
Taking (q=1) (and so (1/q^=0)) in Theorem 7.1 we obtain bigl(Y_{1,lambda}(a,b) bigr)^{-1}=frac{1}{a-b} int_{1}^{a/b}frac {dt}{1-lambda+lambda t^{2}}, which after an elementary computation (by change of variables) yields the desired result.
On the other hand, an elementary computation yields frac{partial u}{partial w}geq0,qquad frac{partial u}{partial z}geq0, qquadfrac{partial v}{partial w}geq0,qquad frac{partial v}{partial z}geq0, which implies that (u=g_{1}(w,z)) is nondecreasing in both w and z, and (v=g_{2}(w,z)) is also nondecreasing in both u and v for all ((u,v geq 0,0)).
An elementary computation gives R Φ ( A, A, A ) = A. Note that here the function Φ is the inverse of the associated function of the homogeneous mean A, i.e., Φ − 1 ( x ) = A ( 1, x ).
As, an elementary calculation shows that (2.10).
The result follows by an elementary calculation.
It remains only some elementary computation.
Elementary computation and (3.6) yield (3.7).
Equation (3.4) and elementary computation yields (3.5).
By elementary computation, we arrive at (4.16).
