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Let f(x) be a real valued function defin...

Let `f(x)` be a real valued function defined for all `xge1`, satistying `f(1)=1` and `f'(x)=1/(x^(2)+f(x))`, then `lim_(xtooo)f(x)`
a. doesn't exist
b.exists and less than `(pi)/4`
c. exists and less than `1+(pi)/4`
d. exists and equal to 0

A

(a) doesn't exist

B

exists and less than `(pi)/4`

C

exists and less than `1+(pi)/4`

D

exists and equal to 0

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
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  2. For n in N, let f(n) (x) = tan ""(x)/(2) (1+ sec x ) (1+ sec 2x) (1+ s...

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  3. Let f(x) be a real valued function defined for all xge1, satistying f(...

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  4. The quadratic equation whose roots are the minimum value of sin^(2)the...

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  5. If x1=sqrt(3) and x(n+1)=(xn)/(1+sqrt(1+x n^2)),AA n in N then lim(n...

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  6. lim(xtoa^(-))(sqrt(x-b)-sqrt(a-b))/((x^(2)-a^(2))),(agtb) is

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  7. lim(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to

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  8. The value of lim(xto0)2/(x^(3))(sin^(-1)x-tan^(-1)x)^(2//x^(3)) equals

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  9. lim(nto oo)sum(r=1)^(n)r/(n^(2)+n+4) equals a. 0 b. 1/3 c. 1/2 d.1

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  10. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10};...

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  11. int(-1)^(2)[([x])/(1+x^(2))]dx, where [.] denotes the greatest integer...

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  12. If alpha and beta are roots of x^(2)-(sqrt(1-cos 2 theta))x+theta=0, w...

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  13. If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim(xto...

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  14. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2ltf(x)lt(x^2|...

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  15. Let f(x) be polynomial of degree 4 with roots 1,2,3,4 and leading coef...

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  16. lim x→π/4 (4sqrt(2)-(cosx+sinx)^5)/(1−sin2x) is equal to

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  17. If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3, the number ...

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  18. Let f(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the...

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  19. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

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  20. Find dy/dx if x^7-e^x=siny

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