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about to only mathematics

A

`f"(x)` exist for all `x in (0,oo)`

B

`f'(x)` exists for all `x in (0,oo)` and `f'` is continuous on `(0,oo)` but not differentiable on `(0,oo)`

C

there exists `alpha gt 1` such that `|f'(x)| lt |f(x)|` for all `x in (alpha, oo)`

D

there exists `beta gt 0` such that `|f(x)| + |f'(x)| le beta` for all `x in (0,oo)`

Text Solution

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The correct Answer is:
B, C
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. The value of underset(xrarr0)(lim)(1)/(x^(3)) int(0)^(x)(tln(1+t))/(t^...

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  2. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

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  3. about to only mathematics

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  4. For any real number x, let [x] denote the largest integer less than or...

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  5. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  6. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  7. Consider the polynomial f(x) = 1+2x+3x^(2)+4x^(3) Let s be the sum...

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  8. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  9. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

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  10. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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  11. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  12. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

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  13. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  14. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  15. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  16. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

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  17. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

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  18. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

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  19. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  20. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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