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find the value of k such that f(x) = 1-cos4x/8x^2,if x is not equal to zero k,if x=0 it is continous at x=0

find the value of k such that
f(x) = 1-cos4x/8x^2,if x is not equal to zero
                     k,if x=0
it is continous at x=0

Grade:11

4 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hi Student,

For the fucntion to be continuous at x=0, f(0+)=f(0-)=f(0)=k

So, Lim(x->0) [1-cos4x/8x^2]
=> Lim(x->0) [2sin22x/8x^2]
=> Lim(x->0) [sin22x/(2x)2]
=> 1

Rasal V
10 Points
9 years ago
K=1.
lim      f(x)=k
X-->0-
 
therefore, lim              1-cos4x/8x^2=sin^2(2x)+cos^2(2x)-cos^2(2x)+sin^2(2x)/8x^2
                 x-->0    
                                                             =1/8 lim  2sinj^2(2x)/x^2
                                                                      x-->0
                                                              =1/8*2*lim      4    since(lim x-->0 sinx/x=1)
                                                                            x-->0
 
therefore k=1/8*2*4=1
Rasal V
10 Points
9 years ago
K=1.
lim      f(x)=k
X-->0-
 
therefore, lim              1-cos4x/8x^2=sin^2(2x)+cos^2(2x)-cos^2(2x)+sin^2(2x)/8x^2
                 x-->0    
                                                             =1/8 lim  2sinj^2(2x)/x^2
                                                                      x-->0
                                                              =1/8*2*lim      4    since(lim x-->0 sinx/x=1)
                                                                            x-->0
 
therefore k=1/8*2*4=1
Rasal V
10 Points
9 years ago
K=1.
lim      f(x)=k
X-->0-
 
therefore, lim              1-cos4x/8x^2=sin^2(2x)+cos^2(2x)-cos^2(2x)+sin^2(2x)/8x^2
                 x-->0    
                                                             =1/8 lim  2sinj^2(2x)/x^2
                                                                      x-->0
                                                              =1/8*2*lim      4    since(lim x-->0 sinx/x=1)
                                                                            x-->0
 
therefore k=1/8*2*4=1

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