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Differential Calculus

Blazing goIITian

 Joined: 1 Apr 2012 Post: 381
10 Aug 2012 13:05:18 IST
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Diff. calculus
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

#### Find the values of a and b so that f(x)={}

b                                ;  x=-2                   }

may be continous at x=-2

{

how explain with steps

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
10 Aug 2012 23:00:48 IST
0 people liked this

hello,

since function is continious at x=2

hence at x=2     l.h.l.=r.h.l=b

for r.h.l.   limx--->-2 x4-16/x5+35  =  4x3/5x4=4/5x=-2/5 (applying L'obtal rule and differenciating)

hence sin x4-16/x5+35 =sin(-2/5)

so b=sin(-2/5)

now for l.h.l.  clearly e1/  = infinity  as x->-2      hence divide numenator and denomenator e1/

and applying limit we get  l.h.l.=-a

-a=b    hence    a=sin2/5

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