Exempelsamling Vektoranalys

5020. 20 Betrakta nivåytan φ = x 2 − 2y 2 − 2z = 0.n P = (gradφ) P = (4, −4, −2). Tangentplanets ekvation blir −2x + 2y + z =−1.21. 21 π/222. 22 s ≈ ∆φ| gradφ| = 3 √510 −623. 23( ) dTdsP 0= (gradT) P0 · e = | gradT| P0 e 0 · e = | gradT| P0 cosα(gradT) P0 = (4, −1, −2)( ) dTdse 0 =( gradT| gradT|)P 0=(4, −1, −2)√21= −2 = | gradT| P0 cosα = √ 21cosαP 0(α = arccos − √ 2 )2124. 24a) 0b) 2πc) π/2d) −1/2e) 5/325. 25 (a) 23(b) 126. 26a) 3/2b) (8π 3 − 2)/327. 27 A = gradxy/z, integralen = −5/3