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If `f(x) =x , x<0` and `f(x)=1 , x = 0,` and `f(x)=x^2,x>0` then `lim_(x->0) f(x)` is equal to

A

0

B

1

C

2

D

does not exist.

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. lim(x -> oo) x^n / e^x = 0, (n is an integer) for

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  2. lim(xrarr0) (x)/(tan^-1x) is equal to

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  3. If f(x) =x , x<0 and f(x)=1 , x = 0, and f(x)=x^2,x>0 then lim(x->0) ...

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  4. Evaluate the following limits : Lim(x to oo) sqrt(((x+sin x)/(x- cos...

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  5. Evaluate: ("lim")(xvecoo)(1+1/(a+b x))^(c+dx),w h e r ea , b , c ,a n ...

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  6. If f'(2)=2, f''(2) =1, then lim(xrarr2)(2x^2-4f'(x))/(x-2), is

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  7. lim(xrarr0) (e^(tanx)-e^x)/(tanx-x)=

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  8. The value of lim(xrarr2^-) {x+(x-[x])^2}, is

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

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  10. The value of lim(x->oo)(pi/2-tan^(- 1)x)^(1/x^2), is

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  11. The value of lim(x->a) (sinx/sina)^(1/(x-a))=

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  12. Evaluate the following limit: (lim)(x->oo)((x^2+2x+3)/(2x^2+x+5))^((3x...

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  13. Evaluate: ("lim")(xvecoo)((a1^( 1/x)+a2^ (1/x)+ --+a n^(1/x))/n)^(n x)

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  14. The value of lim(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx)), is

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  15. lim(x->1)[(x^3+2x^2+x+1)/(x^2+2x+3)]^((1-cos(x-1))/(x-1)^2)

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  16. The value of lim(xrarr0) (sinx)/(xqrt(x^2)), is

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  17. Let f:R to R be a differentiable function such that f(2)=2. Then, the ...

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  18. Let f''(x) be continuous at x = 0 and f"(0) = 4 then value of lim(x->0...

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  19. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

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  20. Find the values of aa n db in order that ("lim")(xvec0)(x(1+acosx)-bsi...

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