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Statement 1: If differentiable function `f(x)` satisfies the relation `f(x)+f(x-2)=0AAx in R ,` and if `(d/(dx)f(x))_(x=a)=b ,t h e n(d/(dx)f(x))_(x=a+4000)=b`. Statement 2: `f(x)` is a periodic function with period 4.

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)d...

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  2. If for some differentiable function f(alpha)=0a n df^(prime)(alpha)=0,...

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  3. Statement 1: If differentiable function f(x) satisfies the relation f(...

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  4. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  5. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),f...

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  6. dy/dx=(sqrt((1-sin2x)/(1+sin2x))) is equal to, 0ltxltpi/2

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  7. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a)(n y)/(sqrt(x^2+a^2...

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  8. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

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  9. (d)/(dx)cos^(-1)sqrt(cosx),0ltxlt(pi)/(2) is equal to

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  10. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

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  11. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

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  12. If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is eq...

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  13. If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a (a)function of x (...

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  14. If y=(log)(sinx)(tanx),t h e n(((dy)/(dx)))(pi/4)"is equal to" (a)4...

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  15. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a)...

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  16. If (lim)(xvec0)(a e^x+bcos x+c e^(-x))/(e^(2x)-2e^x+1)=4,t h e n a.a=...

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  17. If underset(xrarroo)(lim)xlog(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,...

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  18. The value of (lim)(x->(3pi)/4)(1+t a n x1/3)/(1-2cos^2x) is (a)-1//2 (...

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  19. Let f : R rarr R be a differentiable function at x = 0 satisfying f(0)...

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  20. The value of lim(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2...

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