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Show that 1+x ln(x+sqrt(x^2+1))geqsqrt(1...

Show that 1+x ln`(x+sqrt(x^2+1))geqsqrt(1+x^2)` for all `xgeq0.`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
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  2. Find the coordinates of the point on the curve y=x/(1+x^2)where the te...

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  3. Show that 1+x ln(x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

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  4. A swimmer S is in the sea at a distance d km from the closest point A ...

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  5. Find the shortest distance of the point (0, c) from the parabola y=...

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  6. If ax^2+b/xgecfor all positive x where agt0andbgtc show that 27ab^2ge4...

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  7. An extremum of the function f(x)=(2-x)/picospi(x+3)+1/(pi^2)sinpi(x+3)...

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  8. If f(x)a n dg(x) are two positive and increasing functions, then which...

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  9. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

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  10. For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the followi...

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  11. If f(x)=(sin^2x-1)^("n"),"" then x=pi/2 is a point of local maximum, i...

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  12. Let f(x) be an decreasing function defined on (0,oo). If f(3a^2-4a+1)g...

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  13. In which of the following graphs is x=c the point of inflection?

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  14. L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2 Then at x=1/2, whi...

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  15. If composite function f1(f2(f3((fn(x))))n timesis an decreasing functi...

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  16. The function (sin(x+a))/(sin(x+b)) has no maxima or minima if (a) b-a...

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  17. If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)A...

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  18. Which of the following statements is true for the function f(x)={sqrt(...

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  19. If f"(x)>0 for all x in R, f'(3)=0,and g(x)=f(tan^2 x-2tan x+4),0<x<pi...

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  20. Let f(x) be a function such that f'(x)=(log)(1/2)[(log)3(sinx+a)]dot ...

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