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Let f(x) ={:{(x, "for", 0 le x lt1),( 3...

Let `f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):}`
Then f(x) is

A

continuous at x =1

B

Right continuous at x =1

C

Left continuous at x =1

D

Limit exists at x =1

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The correct Answer is:
B
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} The...

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  2. If the function f(x) = (1-x) tan ""(pix)/2 is continuous at x =1 th...

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  3. Let f(x) = {:{ (x sin""(1/x) , x ne 0) , ( k , x = 0):} then f(x)...

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  4. Let {:{((3|x|+4tanx)/x, x ne 0),(k , x =0):} Then f(x) is continu...

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  5. Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):} then f(x) is continu...

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  6. If the function f(x) = (x(e^(sinx) -1))/( 1 - cos x ) is continuous a...

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  7. Let f(x) = (x(2^(x)-1))/( 1- cos x) for x ne 0 what choice of f(0)...

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  8. If f(x)={:{([x]+[-x] , xne 0), ( lambda , x =0):} where [.] denotes...

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  9. If f(x)={((sin[x])/([x]), [x]!=0),(0,[x]=0):} where [.] denotes the ...

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  10. Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

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  11. If f(x) = {:{(px^(2)-q, x in [0,1)), ( x+1 , x in (1,2]):} and f(1...

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  12. let f(x) = {:{( x^(2) , x le 0) , ( ax , x gt 0):} then f (x) is d...

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  13. If f is derivable at x =a,then underset(xto a ) lim( (xf(a) -af( x))/...

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  14. Let f(x) = x|x| then f'(0) is equal to

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  15. If f(x) =|x| , then f'(0) is

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  16. Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x)...

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  17. If f(x )=sqrt(25-x^(2)), then what is underset(xto1)lim(f(x)-f(1))/(x-...

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  18. if f(x)=e^(-1/x^2),x!=0 and f (0)=0 then f'(0) is

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  19. If f(x)=log|x|,xne0 then f'(x) equals

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  20. d/(dx) (sin^(-1) "" (2x)/(1+x^(2))) is equal to

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