1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)f(x) g(x)a) e^x x^2b)e^ x In xc) In x e^xd)x In xe)3^ x 2^ x2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5( 儿)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 08:48:13
1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)f(x) g(x)a) e^x x^2b)e^ x In xc) In x e^xd)x In xe)3^ x 2^ x2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5( 儿)
xOP&]:auK?B&2R!8' B}_iE0%Ӓs>s ^!}ۇ ($xww"#?7.A@^DY`}h;vUN(c  I3YA#M7CXj8uwZ q4xbx~[` d>(x ?"1a<bD$uCDnr+ǻFWN~X٠oi5c= 6'զ9$ݴ1T w0p9wefzJ^'-5U*˸+1eF&3+mS[J3A'dXqG,H-vI|u݋i&Y2Ip"29Zҳ)Dօ+saYmvAA

1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)f(x) g(x)a) e^x x^2b)e^ x In xc) In x e^xd)x In xe)3^ x 2^ x2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5( 儿)
1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)
f(x) g(x)
a) e^x x^2
b)e^ x In x
c) In x e^x
d)x In x
e)3^ x 2^ x
2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5
( 儿)

1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)f(x) g(x)a) e^x x^2b)e^ x In xc) In x e^xd)x In xe)3^ x 2^ x2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5( 儿)
工科留学生为你解答.
1.可以观察到当x->oo,f(x)和g(x)都趋向于正无穷,写成比的形式就可以用洛必达法则(L'Hopital's Role)求极限,我们一个个来看:
a) 用两次洛必达法则,分子为e^x,分母为2,当x->oo时,它们的比值趋近于正无穷而不是0,排除;
b)用一次洛必达法则,分子为e^x,分母为1/x,当x->oo时,是一个趋近于正无穷的数比上一个趋近于0的数,比值趋近于正无穷而不是0,排除;
c) 与b)正好是分子与分母进行了交换,是一个趋近于0的数比上一个趋近于正无穷的数,比值趋近于0,正确;
d)用一次洛必达法则,分子为1,分母为1/x,当x->oo时,比值趋近1/0,即正无穷而不是0,排除;
e)f(x)/g(x)=(3/2)^x,无需用洛必达法则,只要知道指数函数当底数大于1时(这里是3/2),函数值在自变量x趋向于正无穷时也趋向于正无穷,而不是0,排除.
综上,只有c)满足条件.
*以后只要知道函数增长快慢的顺序即可:对数函数(logarithmic function)

用a,chopsticks,you,here's,of,pair,for 造句 1.for which pair(s) of functions will lim x->oo f(x)/g(x)=0?(请详解)f(x) g(x)a) e^x x^2b)e^ x In xc) In x e^xd)x In xe)3^ x 2^ x2let f(x)=xsinx.find an equation for the line tangent to df(x)/dx at x= 派(-)/5( 儿) 连词成句:trousers,here's,pair,for,of,a,you(.) a,gloves,you,here's,of,pair,for.请连成句子 根据首字母填空This pair of red and yellow trainers is s() for the PE lesson. here's a new pair of shoes for you thank you,but there's no need---a new pair for mehere's a new pair of shoes for youthank you,but there's no need---a new pair for meA.to have bought B.to buy C.buying D.to be buying选什么,为什么 Two dollars for one pair. which pair is right汉语是什么意思 His mother bought a pair of pants for him.Do you think it's niceit's or they're It's monstrous to charge that much for a single pair of shoes.的意思It's monstrous to charge that much for a single pair of shoes.这句话的意思是什么啊? On last PE class my friend Zhang Jue put on a pair of new Adidas sports shoes,which attracted my eyes on her feet.I admired her very much for having such a pair of shoes. 第3题 From the moment of a man''s birth,his experience and behavior are shaped by the customs __1____ he is born.1.into which 2.for which 3.at which 4.with which she doesn't know which pair of jeans to buy.both of then look her.A.well on B.seach for C.good at D.beautiful with Which, I fall from the sky,I have a pair of catch people's eyes I'm too!的中文意思? here___is/are___a pair shoes for you The pair of shoes is made ___ and it's suitable ___ going for a walk. A.of,of B,from ,forC.of,for D,from ,of That pair of trousers _____ Kate's? The pair of glass over ______is__________father's.