Bài tập toán cao cấp part 4 pot

... ϕ.Tac´o x 4 + y 4 x 2 + y 2 = ρ 4 (cos 4 ϕ + sin 4 ϕ) ρ 2 (cos 2 ϕ + sin 2 ϕ) = ρ 2 (cos 4 ϕ + sin 4 ϕ). V`ı cos 4 ϕ + sin 4 ϕ  2nˆen lim x→0 y→0 x 4 + y 4 x 2 + y 2 = lim ρ→0 ρ 2 (cos 4 ϕ + sin 4 ϕ)=0. 7.3. ... x 0 nˆe ´ u: 1) f(x)=    4 · 3 x nˆe ´ u x<0 2a + x khi x  0. (DS. H`am f liˆen tu . c ∀x ∈ R nˆe ´ u a =2) 7 .4. Gi´o . iha . n v`a liˆen tu . ccu...

Ngày tải lên: 13/07/2014, 23:20

... lim x→0 1 − x 2 2 + x 4 8 + o(x 4 ) −1+ x 2 2 − x 4 24 +0(x 4 ) x 3 (x +0(x)) = lim x→0 x 4 8 − x 4 24 +0(x 4 ) x 4 +0(x 4 ) = lim x→0 1 8 − 1 24 + o(x 4 ) x 4 1+ 0(x 4 ) x 4 = 1 8 − 1 24 +0 1+0 = 1 12 · ... o(t 2 ) =  − x 2 2 + x 4 24 + o(x 4 ) − 1 2  − x 2 2 + x 4 4 + o(x 4 )  2  + o   − x 2 2 + x 4 24 + o(x 4 )  2  = − x 2 2 + x 4 24...

Ngày tải lên: 13/07/2014, 23:20

... x 2 (DS. 1 2π ) 43 . lim x→0 cos mx − cos nx x 2 (DS. 1 2 (n 2 − m 2 )) 44 . lim x→∞ x 2  cos 1 x − cos 3 x  (DS. 4) 45 . lim x→0 sin(a + x) + sin(a −x) −2sin a x 2 (DS. −sin a) 46 . lim x→0 cos(a ... lim x→−2 x 2 − 4 arctg(x +2) (DS. 4) 38. lim x→0 tgx − sin x x 3 (DS. 1 2 ) 39. lim x→0 xcotg5x (DS. 1 5 ) 40 . lim x→1 (1 − x)tg πx 2 (DS. 2 π ) 41 . lim x→1 1 − x 2 sin πx (DS. 2 π...

Ngày tải lên: 13/07/2014, 23:20

... d[x √ 64 − x 2 ]+d  64arcsin x 8  = xd √ 64 − x 2 + √ 64 −x 2 dx +64d  arcsin x 8  = x d( 64 − x 2 ) 2 √ 64 − x 2 + √ 64 −x 2 dx + 64 d  x 8   1 − x 2 64 = −x 2 dx √ 64 −x 2 + √ 64 − x 2 dx ... f(x)=  ln 2 x − 4. d 2 f ?(DS. 4lnx 4 −ln 3 x x 2  (lnx − 4) 3 (dx) 2 ) 17. f(x) = sin 2 x. d 3 f ?(DS. 4 sin 2x(dx) 3 ) 18. f(x)= √ x −1, d 4 f ?(DS. −15 16(x −1) 7/2...

Ngày tải lên: 13/07/2014, 23:20

... y,x 2 + y 2 ). (D S. u  xx = f  tt +4xf  tv +4x 2 f  vv +2f  v , u  xy = f  tt +2(x + y)f  tv +4xyf  vv , u  yy = f  tt +4yf  tv +4y 2 f  vv +2f  v , t = x + y, v = x 2 + ... y 2 ∂ 2 u ∂y 2 = n(n −1)u. 44 . u = f(x + g( y)), ∂u ∂x · ∂ 2 u ∂x∂y = ∂u ∂y · ∂ 2 u ∂x 2 · 45 . T`ım da . o h`am theo hu . ´o . ng ϕ = 135 ◦ cu ’ a h`am sˆo ´ f(x, y)=3x 4 + xy + y 3 ta . i...

Ngày tải lên: 13/07/2014, 23:20