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If lim(x->oo) f(x) exists and is finite...

If `lim_(x->oo) f(x)` exists and is finite and nonzero and if `lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3`,then find the value of `lim_(x->oo) f(x)`

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Verified by Experts

The correct Answer is:
`(1)`
`underset(xtooo)lim(f(x)+(3f(x)-1)/(f^(2)(x)))=3`
or `(underset(xtooo)limf(x)+(3underset(xtooo)limf(x)-1)/((underset(xtooo)limf(x))^(2)))=3`
or `(y+(3y-1)/(y^(2)))=3`
or `y^(3)-3y^(2)+3y-1=0`
or `(y-1)^(3)=0`
or `y=1`
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CENGAGE PUBLICATION-LIMITS-Numerical Value Type
  1. lim(xtooo) f(x)," where "(2x-3)/(x)ltf(x)lt(2x^(2)+5x)/(x^(2))AAxgt0,"...

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  2. If f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1,xlt=0,a n dh(x) ...

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  3. If lim(x->oo) f(x) exists and is finite and nonzero and if lim(x->oo)...

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  4. If L-("lim")(xvec2)((10-x)^(1/3)-2)/(x-2),t h e nt h ev a l u eof|1(4L...

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  5. If lim(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1, then the value of p is.

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  6. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

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  7. If L= lim(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)), then the value of 1/...

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  8. The value of lim(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x) is .

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  9. The value of lim(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is .

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  10. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

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  11. The value of lim(x to oo ) (log(e)(log(e)x))/(e^(sqrt(x))) is . (a) π...

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  12. Find k if x = 3 is a root of equation kx^2 – 10x + 3 = 0

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  13. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

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  14. Let Sn=1+2+3++n and Pn=(S2)/(S2-1)dot(S3)/(S3-1)dot(S4)/(S4-1)...(Sn)...

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  15. If lim(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| is.

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  16. Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a). Then the value of f(4) ...

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  17. Number of integral values of k for which lim(xto1) sin^(-1)((k)/(log...

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  18. If lim(xto1) (1+ax+bx^(2))^((c)/((x-1)))=e^(3), then find the value of...

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  19. Let f ''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))...

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  20. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then find the value o...

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