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Statement 1: For f(x)=sinx ,f^(prime)(pi...

Statement 1: For `f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi)dot` Statement 2: For `f(x)=sinx ,f(pi)=f(3pi)dot`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

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  2. Statement 1: Let f: R -> R be a real-valued function AAx ,y in R such...

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  3. Statement 1: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi)dot Statement...

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  4. f:R^+ ->R is a continuous function satisfying f(x/y)=f(x)-f(y) AAx,y i...

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  5. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)...

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  6. Suppose f and g are functions having second derivative f'' and g' ' ev...

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

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

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

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

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

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

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

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

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  17. 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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  18. 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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  19. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a)-(cosx+si...

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  20. 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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