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Question

If the function f(x)=ex2cosxx2 for x0 continuous at x=0 then f(0)=

A
12
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B
32
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C
2
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D
13
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Solution

The correct option is B 32
Here , function is continuous ,
So, left limit and right limit boh are equal and equals to the value of f(x) at x=0
Therefore
limx0f(x)=limx0ex2cosxx2
Solving limit by derivative approach,
=> limx0f(x)=limx0ex2.2x+sinx2x
=> limx0f(x)=limx02ex2+ex2.x2+cosx2x
Putting x=0, we get
=> f(0)=2+0+12=32

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