find the value of k given function is continious at x=0
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k=±1
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as value at x(+/-)h is equal to value at x then it's continuous. as value at x=0 is f(x)=1/2.
for right hand limit x+h=h as x=0 given
f(Rhl)=lim (h->0) 1-coskh/h*sinh as it is 0/0 form
so by using L'hospital rule f =lim(h->0) sinkh*k/hcosh+sinh again 0/0 form again differentiate f=coskh*k²/cosh-hsinh+cosh now apply the limit h->0 and equate it to value at x=0 i.e 1/2
for right hand limit x+h=h as x=0 given
f(Rhl)=lim (h->0) 1-coskh/h*sinh as it is 0/0 form
so by using L'hospital rule f =lim(h->0) sinkh*k/hcosh+sinh again 0/0 form again differentiate f=coskh*k²/cosh-hsinh+cosh now apply the limit h->0 and equate it to value at x=0 i.e 1/2
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