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Let f(x) be a function defined on (-a ,a...

Let `f(x)` be a function defined on `(-a ,a)` with `a > 0.` Assume that `f(x)` is continuous at `x=0a n d(lim)_(xvec0)(f(x)-f(k x))/x=alpha,w h e r ek in (0,1)` then a. `f^(prime)(0^+)=0` b. `f^(prime)(0^-)=alpha/(1-k)` c. `f(x)` is differentiable at `x=0` d. `f(x)` is non-differentiable at `x=0`

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Consider two functions y=f(x) and y=g(x) defined as f(x)={[a x^2 +b...

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

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

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

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

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

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

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

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

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

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

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  15. If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x...

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  16. Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):}. If f...

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  17. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

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  18. Let f(x)=[t a n x[cot x]],x [pi/(12),pi/(12)] , (where [.] denotes the...

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  19. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

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  20. If g(x)=(lim)(mvecoo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e...

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