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let f(x)=x^3-x^2-3x-1 , g(x)=(x+1)aand h...

let `f(x)=x^3-x^2-3x-1 , g(x)=(x+1)a`and `h(x)=f(x)/g(x)` where `h` is a rational function such that `(1)` it is continuous everywhere except when `x=-1 ,(2) lim_(x->oo)h(x)=oo ` and `(3) lim_(x->-1)h(x)=1/2` then the value of `h(1)`

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f(x)=x^(3)-x^(2)-3x-1,g(x)=(x+1)a and h(x)=(f(x))/(g(x)) where h is a rational function such that (1) it is continuous everywhere except when x=-1,(2)lim_(x rarr oo)h(x)=oo and (3) lim_(x rarr-1)h(x)=(1)/(2) then the value of h(1)

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MOTION-CONTINUITY -EXERCISE - 3
  1. If the function f(x)=(3x^2+ax+a+3)/(x^2+x-2) is continuos at x=-2 .Fin...

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

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  3. If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...

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  4. Let [x] denote the greatest integer function & f(x) be defined in a ne...

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  5. Let f(x) = [{:((pi/2.sin^(-1)(1-x^(2))sin^(-1(1-{x})))/(sqrt(2((x)-(x)...

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  6. Find all possible values of a and b so that f(x) is continous for all ...

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  7. Draw the graph of the function f(x) = x - |x - x^(2)|, -1 le x le 1 an...

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  8. Discuss the continuity of 'f' in [0, 2], where f(x) = {{:(|4x - 5|[x],...

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  9. let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(l...

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  10. Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof)...

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  11. The function f(x)= ((2+ cos x)/(x^(3) sin x)-3/x^(4)) is not defined a...

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  12. The function f(x) = [{:((6/5)^(tan 6x)/(tan 5x), if, 0 lt x lt pi/2),(...

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  13. Determine a & b so that f is continuous at x = pi/2 whre f(x) = [{:(...

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  14. Determine the values of a , b , c for which the function f(x)={(sin(a+...

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  15. If f(x) = (Sin 3x + A sin 2x + B sinx)/x^5 for x != 0is continuous a...

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  16. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

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  17. Given the function g(x) = sqrt(6-2x) and h(x) = 2x^(2) - 3x + a. Then ...

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  18. f(x) = {{:((a^(sin x)-a^(tanx))/(tan x-sin x), "for",x gt 0),((ln(1+x+...

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  19. let f(x)=x^3-x^2-3x-1 , g(x)=(x+1)aand h(x)=f(x)/g(x) where h is a rat...

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