A) \[3\]
B) \[10\]
C) \[13\]
D) \[5\]
Correct Answer: D
Solution :
We have, \[h(x)={{[f(x)]}^{2}}+{{[g(x)]}^{2}}\] On differentiating w.r.t.\[x,\] we get \[h'(x)=2f(x)f'(x)+2g(x)g'(x)\] ? (i) Given that, \[f''(x)=-f(x)\] and \[f'(x)=g(x)\] ? (ii) On differentiating Eq. (ii), we get \[f''(x)=g'(x)\] \[\Rightarrow \] \[g'(x)=-f(x)\] From Eq. (i) \[h'(x)=2f(x)-f'(x)-2f'(x)f(x)\] \[=0\] \[\Rightarrow \] \[h(x)=5\] \[[\because \,\,h(5)=5]\] \[\therefore \] \[h(10)=5\]You need to login to perform this action.
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