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Let f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x...

Let `f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x=4),((x-4)/(|x-4|)+b ,x >4):}` Then `f(x)` is continous at `x=4` when a.`a=0,b=0` b. `a=1,b=1` c. `a=-1,b=1` d. `a=1,b=-1`

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RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. If u=f(x),v=g(x), then the value of D^*(udotv) is (D^*u)v+(D^*v)u b. u...

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  3. Let f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x=4),((x-4)/(|x-4|)+b ,x >4):} ...

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  4. If f(x)=x^3+bx^2+cx+d and 0 < b^2 < c, then in (-oo,oo), (a) f(x) is...

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  5. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

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  6. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive func...

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  7. Let f:(-1,1)vecR be a differentiable function with f(0)=-1 and f^(prim...

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  8. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

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  9. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

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  10. If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

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  11. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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  12. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)),w h e r eprod(i=1)^k ai st...

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  13. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

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  14. 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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  15. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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  16. Find (dy)/(dx) in each of the following cases: y=tan^(-1)(4x)/(1+5x^2...

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  17. If f(x)=lim(n-&gt;oo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) whe...

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  18. If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R...

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  19. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  20. If y=x/(a+x/(b+x/(a+oo))),t h e nfin d(dy)/(dx)

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