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Let f(x)={lim(n->oo)(a x(x-1)(cot((pix)...

Let `f(x)={lim_(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/4))^n+1) ,x in (0,1) uu (1,2) and 0 ,x=1` If f(x) is differentiable for all `x in (0, 2)` then `(a^2 +p^2)` equals

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is cont...

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  2. Let f(x)=(lim)(n rarr oo)sum(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (...

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  3. Let f(x)={lim(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/...

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  4. If f(x)={(sinx, x != npi " and " n in I2), (2, " x=npi):} and g(x)={(x...

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  5. The number of points at which g(x)=1/(1+2/(f(x))) is not differentiabl...

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  6. If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is a. x...

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  7. Consider two functions y=f(x) and y=g(x) defined as f(x)={[a x^2 +b...

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  8. Let f be a function with continuous second derivative and f(0)=f^(prim...

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  9. Let f(x) be a function defined on (-a ,a) with a > 0. Assume that f(x)...

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  10. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

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  11. Let f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)...

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  12. For which of the following functions f(0) exists such that f(x) is con...

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  13. Let f(x)=x^(3)-x^(2)-3x-1, g(x)=(x+1)a and h(x)=(f(x))/(g(x)) where h...

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  14. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

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  15. If f(x)={sin(pi/2)(x-[x]),x<5 5(b-1),x=5(a b^2|x^2-11 x+24|)/(x-3),x >...

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  16. The function f(x) is discontinuous only at x=0 such that f^2(x)=1AAx i...

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  17. f(x)={(x^2+e^(1/(2-x)))^(-1)k ,x=2, x!=2 is continuous from right at t...

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  18. If the function f(x)=((128 a+a x)^(1//8)-2)/((32+b x)^(1//5)-2) is con...

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  19. If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 is continous at x=0 the...

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  20. f is a continous function in [a, b]; g is a continuous function in [b,...

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