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f(x)={|x - 4| for x leq 1 x^3/2-x^2+3x...

`f(x)={|x - 4| for x leq 1 x^3/2-x^2+3x+1/2 for x lt 1` , then 1) f(x) is continuous at x=1 and x=4 2) f(x) is differentiable at x=4 3) f(x) is continuous and differentiable at x=1 4) f(x) is only continuous at x=1

A

f(x) is continuous at x=1 and x=4

B

f(x) is differentiable at x=4

C

f(x) is continuous and differentiable at x=1

D

f(x) is not continuous at x=1

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  3. f(x)={|x - 4| for x leq 1 x^3/2-x^2+3x+1/2 for x lt 1 , then 1) ...

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  4. Let f(x) ={(sin2x , if 0leqxleqpi/6),(ax+b , if pi/6ltxlt1):} If f(x...

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  5. Let f(x)={(int(0)^(x){5+|1-t|}dt, "if" xlt2),(5x+1, "if" xge2):} then:

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  6. The function f defined by f(x)={{:(,(sinx^(2))/(x),x ne 0),(,0,x=0):} ...

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  7. If f(x) is continuous at x=0 and f(0)=2, then underset(x to 0)lim unde...

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  8. If f(x) defined by f(x)={(|x^2-x|)/(x^2-x1,x=0),x!=0,1-1,x=1 then (...

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  9. If f(x)={(1-sinx)/((pi-2x)^2)dot(logsinx)/((log(1+pi^2-4pix+4x^2))),x...

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  10. The set of points of differentiable of the function f(x)={{:(,(sqrt(x+...

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  11. The set of points where the function f(x)=|x-1|e^(x) is differentiable...

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  12. If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to

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  13. If f(x)={{:(,(sqrt(x+1)-1)/(sqrtx),"for "x ne 0),(,0,"for x=0):} and f...

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  14. The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0 0,x=0 is continuous a...

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  15. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

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  16. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

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  17. If the function f(x)=|x|+|x-1|, then

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  18. Let f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|)\ \ \ \ ,\ \ \ x!=1,\ 1 6\ \ \ \ ...

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  19. If the function f as defined below is continuous at x=0find the values...

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  20. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

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