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Question

Let f be a twice differentiable such that f′′(x)=f(x) and f(x)=g(x). If h(x)={f(x)}2+{g(x)}2, where h(5)=11. Find h(10)

A
1
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B
10
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C
11
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D
100
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Solution

The correct option is D 11
h(x)=2f(x)×f(x)+2g(x)g(x)

g(x)=f(x)

g(x)=f(x)=f(x)

h(x)=2f(x)f(x)2g(x)f(x)

h(x)=2f(x)g(x)2g(x)f(x)

=0


h(x)=0

ddxh(x)=0

d h(x)=0×dx

h(x)=0+c

h(x)=c

now, h(5)=11

h(10)=h(5)=11

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