Limit Continuity and Differentiability 7 Question 21

21. Let f:RR be any function. Define g:RR by g(x)=|f(x)|,x. Then, g is

(2000,2M)

(a) onto if f is onto

(b) one-one if f is one-one

(c) continuous if f is continuous

(d) differentiable if f is differentiable

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Answer:

Correct Answer: 21. (a)

Solution:

  1. Given, xexy=y+sin2x

On putting x=0, we get

0e0=y+0y=0

On differentiating Eq. (i) both sides w.r.t. x, we get

1exy+xexyxdydx+y=dydx+2sinxcosx

On putting x=0,y=0, we get

e0+0(0+0)=dydx(0,0)+2sin0cos0dydx0,0=1



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