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Let f(x)={{:(-2",",-3lexle0),(x-2",",0lt...

Let `f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)|` What is the value of differential coefficent of g(x) at x=-2

A

-1

B

0

C

1

D

2

Text Solution

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The correct Answer is:
B
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NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

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  2. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

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  3. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

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  4. What is lim(xto0)(e^(x)-(1+x))/(x^(2)) equal to?

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  5. The function f:XtoY defined by f(x)=cosx where x""inX, is one-one and ...

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  6. If f(x)=(x)/(x-1), then what is (f(a))/(f(a+1)) equal to?

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  7. Let f:[-6,6]toR be defined by f(x)=x^(2)-3. Consider the following : ...

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  8. Let f(x)=px+qandg(x)=mx+n." Then "f(f(x))=g(f(x)) is equivalent to

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  9. If F(x)=sqrt(9-x^(2)), then what is lim(xto1) (F(x)-F(1))/(x-1) equal ...

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  10. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

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  11. Let f(x) be defined as follows : f(x)={{:(2x+1",",-3ltxlt-2),(x-1","...

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  12. Consider the following statements : 1. If lim(xtoa) f(x) and lim(xto...

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  13. Let f(a)=(a-1)/(a+1) Consider the following : 1. f(2a)=f(a)+1 2....

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  14. Suppose the function f(x)=x^(n),n!=0 is differentiable for all x. Then...

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  15. The inverse of the function y=5^(Inx) is

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  16. A function is defined as follows : f(x)={{:(-(x)/(sqrtx^(2))",",xne0...

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  17. Consider the following : 1. x+x^(2) is continuous at x=0 2. x+cos(...

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  18. A function is defined in (0,oo) by f(x)={{:(,1-x^(2)," for ",0ltxle1...

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  19. Consider the following statements : 1. Derivative of f(x) may not ex...

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  20. The function f(x)=|x|-x^(3) is

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