高數(shù)課件版-復(fù)習(xí)第二章

華東2010-2011學(xué)年《高等數(shù)學(xué)1f

A，則

f(x03x)f(x0)3函數(shù)fx x在點(diǎn)x0處的導(dǎo)數(shù)f'03fxxx1x1f'1fxsinxx0f'0f(x)(x1)(x2)(x3)(xn)（其中n為正整數(shù)f'(0)y1xexx0yfxx2，則f'fxy

f(x)，且

f(x0f(x02h)3，則dy

xx0yx2exy"(0)d2設(shè)xa(tsint)，ya(1cost)， 設(shè)0x1，則x1t

x

曲線

yt

在t2y2x1xxyxy)y

1arctan2xdyx4xxf(x是可導(dǎo)函數(shù)，且

f(x0hf(x0)1f'(x f(xx1f'(1)2，則

f(1x)f(1x)x ② ③ ④fxx3x0 函數(shù)fx在區(qū)間a,b內(nèi)連續(xù)是fx在a,b內(nèi)可導(dǎo) f(xf(x①奇函 f(xg(x)f(xf(xg'x①奇函 1yf(xf'(x0)2，則當(dāng)x0xx0處的微分dy1①與x等價(jià)的無(wú)窮 ②與x同階的無(wú)窮小，但不等③與x低階的無(wú)窮 ④與x高階的無(wú)窮 x 函數(shù)f(x)1e ，在x0

x①不連 ③可導(dǎo)，且f'(0)f(x)xlnxx0f(x0)2f(x0)① ② ④e設(shè)e2xf(xf(x)

f'(0)①e2

②

③ f(0)2x0f(xf(0x 12f(xF(x)f(x)(1|sinx|f(0)0F(xx0可導(dǎo)的①充要條 13f(xx0

ydy等于 ①- ② ④x x 1x設(shè)x x 1xy

xsin dyyexsinxcosxyyxsinlnxcoslnx，求yarccos1x2，求y3xx3xsin3x1xyxarctan1xx

，求yx1 xx1x1 xx1 xf(x)x(x1)(x2)(x100)，求fyxsinx1 xex x1x設(shè)yarctan(x32) x1xyx6x21)3x2)2(x1)24x(x1)24x3(x1yxx（x0y1x2sinx由lnx2y2exy1yxy(xyexxeyyxxyycot(xyylnyx0由ex2y2sinxy)5yxy(xyy(x由方程lnyx2x3ysinxdxxyarctany0yy(xx3y33axy0（a0）yy(x的微分y(x是由方程sinyxey0y，以及該方程所表示的曲線在點(diǎn)(00)處切線的斜率。d2dxyy(xyf[xgyfd2dx yy(x由方程exe2tcos2

xy0

x設(shè)ye2tsin2t，求1

yy(xx1s22y1s22xecos2 設(shè)yesin2txetcost 設(shè)ye2tsint x 若參數(shù)方程為yt23t2dx在t0x2sin d2設(shè)yetln2dxxe d2設(shè)ytetdxx d2設(shè)ytetdxxtsint設(shè)曲線方程為ytcos

d2x2dxf(x在[01y設(shè)曲線方程為x3y3x1

f(sin2xf(cos2x90x1 設(shè)f(x)3|ax|，求ff(x)xkln(1f(x)

xx0xx0，當(dāng)kx0f(x esin

x

fy

f(x)是奇函數(shù)且在點(diǎn)x0處可導(dǎo)，則點(diǎn)x0是函數(shù)F(x) x

2ex

x11試確定常數(shù)a,bf(x)x211

xx驗(yàn)證