Beijing Normal University Mathematical Analysis (762) recalls the 2018 edition

1 seeking f (x) = xsin (lnx ) derivative and second derivative

2 demonstrates that f (x) = (1 + 1 / x) ∧x in (0, + ∞) monotonic increasing

3 seeking f (x) = x∧2 + y∧3-3xy extreme point extremum and


4 provided trigonometric series a0 / 2 + Σ (ancosnx + bnsinnx) uniformly converges on R f (x), proof
(i) for k∈N , stages

a0coskx / 2 + Σ (ancosnx + bnsinnx) coskx uniform convergence on R

a0coskx / 2 + [Sigma (ancosnx + bnsinnx) sinkx uniform convergence on R

(II)
AN =. 1 / π∫ (0,2) F (X) cosnxdx
BN =. 1 / π∫ (0,2) F (X) sinnxdx

. 5 by the region Ω x∧2-2x = Y, X + Y = 2,
Z = X + Y, Z = 0 enclosed,
(i) the ∫∫∫Ω | xyz | dxdydz written and several repeated integral (not integrand absolute value)
(II) as set Ω0 {P: P∈Ω, x≥0, y≥0 }, seeking ∫∫∫Ω0 | XYZ |. dxdydz

. 6 demonstrate
(i) f (x) = xarctanx + (sinx) ∧2 uniformly continuous in the R

(II)
F (X) = X [arctan (X)] (SiNx) ∧ - 2 inconsistency on successive R & lt

. 7 shows two quaternions function F. (X, Y, U, V), G (X, Y, U, V),
(I) in claim prove (1 / 2,0, 1 / 2,0) may be determined at a neighborhood group implicit function U (x, Y), v (x, Y)
(II) find the partial derivative of x, v, and the second order partial derivative vxx

Provided 8 f (x) is a [0,1] continuous positive function, for n∈N +, proof of
(i) there is a unique an∈ (1 / n, 1) so that
∫ (1 / n, an) f (X) = ∫ DX (AN,. 1) F (X) DX
(II) → LiMn limit exists ∞an

 

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 1 seeking f (x) = xsin (lnx ) derivative and second derivative

2 demonstrates that f (x) = (1 + 1 / x) ∧x in (0, + ∞) monotonic increasing

3 seeking f (x) = x∧2 + y∧3-3xy extreme point extremum and


4 provided trigonometric series a0 / 2 + Σ (ancosnx + bnsinnx) uniformly converges on R f (x), proof
(i) for k∈N , stages

a0coskx / 2 + Σ (ancosnx + bnsinnx) coskx uniform convergence on R

a0coskx / 2 + [Sigma (ancosnx + bnsinnx) sinkx uniform convergence on R

(II)
AN =. 1 / π∫ (0,2) F (X) cosnxdx
BN =. 1 / π∫ (0,2) F (X) sinnxdx

. 5 by the region Ω x∧2-2x = Y, X + Y = 2,
Z = X + Y, Z = 0 enclosed,
(i) the ∫∫∫Ω | xyz | dxdydz written and several repeated integral (not integrand absolute value)
(II) is provided Ω0 P { ∈Ω, x ≧ 0, y ≧ 0}, seeking ∫ ∫∫Ω0 | XYZ |. dxdydz

. 6 demonstrate
(i) f (x) = xarctanx + (sinx) ∧2 uniform continuous in the R & lt

(II)
F (X) = X [arctan (X)] (SiNx) in ∧2 inconsistency on successive R

7 gives two quaternions function F. (X, Y, U, V), G (X, Y, U, V),
(I) in claim prove (1 / 2,0,1 / 2,0) may be determined at the neighborhood of the implicit function group u (x, y), v (x, y)
the partial derivative (ii) to find v x, and the second order partial derivative VXX

. 8 provided f (x) is a [0,1] continuous positive function, for n∈N +, prove
there is a unique an∈ (i) (1 / n, 1) so that
∫ (. 1 / n-, AN) F (X) = ∫ DX (AN,. 1) F (X) DX
(II) is present limn → ∞an limit
source: Beijing Normal University, 2018 mathematical analysis (762) recalls version