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With the help of Lagrange's formula, pro...

With the help of Lagrange's formula, prove that `(a-b)/(a) le log (a/b) le (a-b)/(b)`, for the condition `0 lt b le a.`

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Statement-1 : For 0 le p lt 1 and for any positive a and b the intequality (a+b)^p lt a^p+b^p is valid Staement - 2: For 0 le ple 1 the function f(x)=1 +x^p -(1+x)^p decreases on [0,oo)

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -2
  1. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

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  2. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

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  3. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

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  4. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  5. With the help of Lagrange's formula, prove that (a-b)/(a) le log (a/b)...

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  6. The function f(x)=int(0)^(x)sqrt(1-t^(4)) dt is such that

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

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  8. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

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  9. If f(x) is a cubic polynomial which has local maximum at x=-1,If f(2...

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  10. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

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  11. The maximum value of the function f(x)=3x^(3)-18x^(2)+27x-40 on the s...

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  12. If the function f(x)=x^(4)+bx^(2)+8x+1 has a horizontal tangent and a...

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  13. Let p(x) be a real polynomial of least degree which has a local maximu...

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  14. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

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  15. If the function f:[0,4]vecR is differentiable, the show that for a , b...

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  16. For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...

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  17. A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It it...

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  18. Function f(x), g(x) are defined on [-1, 3] and f''(x) > 0, g''(x) > 0 ...

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  19. If a << b << c << d and x in R then the least value of the function,...

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  20. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

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