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Statement 1: Leg f(x)=x[x]a n d[dot] den...

Statement 1: Leg `f(x)=x[x]a n d[dot]` denotes the greatest integral function, when `x` is not an integer, then rule for `f^(prime)(x)` is given by `[x]dot` Statement 2: `f^(prime)(x)` does not exist for any `x` integer. (a)Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1. (b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. (c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. (d)STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If y=e^(-x)cosxa n dyn+kn y=0,w h e r eyn=(d^(n y))/(dx^n)a n dkn are ...

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  2. If a function is represented parametrically by the equations x=(1+log(...

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  3. Statement 1: Leg f(x)=x[x]a n d[dot] denotes the greatest integral fun...

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  4. Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even ...

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  5. If y=a e^(m x)+b e^(-m x), then (d^(2y))/(dx^2) is equals to

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  6. If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]...

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  7. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a)x/(...

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  8. (d^n)/(dx^n)(logx)=? (a)((n-1)!)/(x^n) (b) (n !)/(x^n) (c)((n-2)!)/(...

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  9. If y="sec"(tan^(-1)x),t h e n (dy)/(dx) at x=1 is (a)cos(pi/4) (b)...

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  10. The differential coefficient of f((log)e x) with respect to x , where ...

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  11. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

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  12. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is ...

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  13. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a)-(cosx+si...

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  14. If x=tcost ,y=t+sint . Then (d^2 x)/(dy^2)at t=pi/2 is (a)(pi+4)/2...

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  15. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

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  16. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  17. f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x. Also,f(3)=5 and...

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  18. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

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  19. Each question contains statements given in two columns which have t...

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  20. Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)d...

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