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The function f(x)=e^(|x|) is (a) Contin...

The function `f(x)=e^(|x|)` is (a) Continuous everywhere but not differentiable at `x = 0` (b) Continuous and differentiable everywhere (c) Not continuous at `x = 0` (d) None of the above

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. If f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 ,\ \ \ \ \ \ \ \ \ \ \ \ ...

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  2. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

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  3. The function f(x)=e^(|x|) is (a) Continuous everywhere but not differ...

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  4. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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  5. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

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  6. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

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  7. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

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  8. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

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  9. If f(x)=|(log)e|x|| , then (a)f(x) is continuous and differentiable ...

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  10. Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is c...

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  11. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

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  12. Let f(x)={a x^2+1,\ \ \ \ \ x &gt;1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 ...

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  13. Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. ...

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  14. Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x)...

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  15. The function f(x)=1+|cosx| is (a) continuous no where (b) continuou...

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  16. The f(x)=|cosx| (a)Then, f ( x ) is everywhere differentiable at x=(...

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  17. The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the gre...

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  18. Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Th...

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  19. If f(x)=|3-x|+[3+x] , where [x] denotes the least integer greater th...

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  20. If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , the...

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