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The largest value of the non-negative in...

The largest value of the non-negative integer a for which `lim_(xrarr1){(-ax+sin(x-1)+a)/(x+sin(x-1)-1)}^((1-x)/(1-sqrtx)}= 1/4

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

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  2. Letf:RrarrR and g:RrarrR be respectively given by f(x)=|x|+1 and g(x)=...

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  3. The largest value of the non-negative integer a for which lim(xrarr1){...

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  4. Let f1:RrarrR,f2:[0,infty)rarrR,f3:RrarrRandf4:Rrarr[0,infty) be defin...

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  5. lim(xrarr0)sin(picos^2x)/x^2 is equal to :

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  6. If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i ...

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  7. The function f(x)=tan{pi[x-pi/2]}/(2+[x^2] , where [x] denotes the gre...

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  8. Let f(x) be a differentiable function and f'(4)=5. Then lim(xrarr2)(f...

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  9. The value of lim(xrarr0)(int0^(x^2) cos(t^2)dt)/(xsinx) is

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  10. If lim(xrarr0)(2asinx-sin2x)/tan^3x exists and is equal to 1, then the...

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  11. The function f(x)=a sin |x| +be^|x| is differentiable at x=0 when

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  12. let f(x)={( int0^x|1-t|dt, xgt1),(x-1/2, xle1):} then

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  13. The number of points in (-infty,infty) , for which x^3-xsin x-cos x =0...

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  14. lim(xrarr0)((1-cos2)(3+cos x))/(xtan 4x) is equal to

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  15. The limit of xsin (e^(1//x)) as xrarr0

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  16. Let f(x)={f(x={(x^3-3x+2, xlt2),(x^3-6x^2+9x+2, xge2):} Then

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  17. The limit of sum(n=1)^1000(-1)^n x^n as xrarrinfty

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  18. The limit of [1/x^2+(2013)^x/(e^x-1)-1/(e^x-1)] as xrarr0

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  19. The limit of {1/xsqrt(1+x)-sqrt(1+1/x^2} as xrarr0

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  20. If lim(xrarrinfty)((x^2+x+1)/(x+1)-ax-b)=4 ,then

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