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Let f"":""RvecR be a function defined...

Let `f"":""RvecR` be a function defined by `f(x)""=""M in""{x""+""1,""|x|""+""1}` . Then which of the following is true? (1) `f(x)geq1""for""a l l""x in R""(2)""f(x)` is not differentiable at `x""=""1` (3) f(x) is differentiable everywhere (4) f(x) is not differentiable at `x""=""0`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2]. If f(x) is ...

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  2. The function f(x)=|x|+|x-1| is Continuous at x=1, but not differentiab...

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  3. Let f"":""RvecR be a function defined by f(x)""=""M in""{x""+""1,""...

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  4. The function f:""R""~""{0}vecR given by f(x)=1/x-2/(e^(2x)-1) ca...

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  5. If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f^(2)(4)...

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  6. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)),w h e r ea , b , c in R ~{0},e ...

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  7. ("lim")(xvecpi/2){(x^3+1)/(x^2+1)-(a x+b)}=2,t h e n a=1,b=1 (b) a=1...

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  8. ("lim")(xvec0)(sinx^n)/((sinx)^m),(m<n),i se q u a lto 1 (b) 0 (c)...

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  9. ("lim")(xvecoo)(1/e-x/(1+x))^xi se q u a lto e/(1-e) (b) 0 (c) e/...

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  10. ("lim")(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1))i se q u a lto ...

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  11. ("lim")(xvecoo)(2sqrt(x)+3x3+4x4++n x n)/(sqrt((2x-3))+(2x-3)3++(2x-3)...

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  12. The value of ("lim")(xvecoo)(cos"x"/"m")^("m") is 1 (b) e (c) e^(-1...

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  13. If f(x)=("lim")(xvecoo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equa...

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  14. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  15. ("lim")(xvecoo)"{"(n/(n+1))^(alpha)+s in1/n"]"^n(w h e nalpha in Q)i ...

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  16. Let f(x)=("lim")(xvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot Then the set of...

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  17. ("lim")(xvec0){(1+x)^(2/x)} (where {.} denotes the fractional part of ...

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  18. lim(x->0) sin(x^2)/(ln(cos(2x^2-x)) is equal to

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  19. If f(x)={x^nsin(1/(x^2)),x!=0 0,x=0,(n in I),t h e n ("lim")(xvec0)...

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  20. (lim)(x->0)((1^x+2^x+3^x++n^x)/n)^(1/x)\ is equal to (n\ !)\ ^n b. (n...

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