Use the Comparison Theorem to determine whether the integral is convergent or divergent. {eq}\int_{1}^{\infty}\frac{1+\textrm{sin}^2x}{\sqrt{x}}dx {/eq} Comparison Test If {eq}f(x)\geq g(x)\geq 0 {/eq} for {eq}x\geq a...
Use the Intermediate Value Theorem to show that the following equation has a solution on the given interval: - x^3 + 6 x^2 - 5 x = 3: over an interval [-1, 5]. Using the Intermediate Value Theorem to prove that the equation has a solution i...
Use the intermediate value theorem to determine whether there is a zero f(x)=−3x3−6x2+10x+9;[−1,0] At Least One Zero: When we work with continuous functions over an interval where, at the extremes, the sign of the function varies, thanks ...
How To: Given a polynomial function f(x)f(x), use the Rational Zero Theorem to find rational zeros. Determine all factors of the constant term and all factors of the leading coefficient. Determine all possible values of pqpq, where p is a factor of the constant term and q is...
and the Fresnel diffraction and Poynting theorem in the paraxial and weak-defocusing approximation13. The gradient and curvature of the phase together determine the wavefront shape, whose normal vector is then parallel to the wavevector at each point of the wavefront, and consequently to the direc...
(The formula is easily shown using the divergence theorem.) The axial drive velocity field is divergence-free, so the last term vanishes. If η is constant in space, also the second-to-last term vanishes, and we have ∫φ:η:[(a·∇)ε] dx = ∫ (a·n) (φ:η:ε) dΓ - ...
A t test assumes your data follow anormal distribution. However, due to the central limit theorem, you can waive this assumption when your sample is large enough. The following sample size guidelines specify when normality becomes less of a restriction: ...
A third factor that might influence the treatment effects is the husband’s unmet need for FP which combines his fertility preferences and awareness of contraceptive use. In particular, if the husband has an unmet need for FP while the wife does not (either because of differences in fertility ...
Answer to: Use Rolle's theorem to determine whether it is possible for the function f(x) = 9x^7 + 4x - 19 to have two or more real roots. By...
Factor out the constant $$\displaystyle 2 \int_1^\infty \dfrac {1} {5n - 1} dn $$ Now we can use Integration by Parts, where {eq}\displaystyle u... Learn more about this topic: Convergence vs. Divergence | Theorem, Function & Examples ...