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Show that (a sin x + b cos x)/(a cos x -...

Show that `(a sin x + b cos x)/(a cos x - b sin x)` increases with x.

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AAKASH SERIES-MAXIMA AND MINIMA -Advanced Subjective Type Questions
  1. If x gt 0, show that log(1+x) - (2x)/(2+x) is increasing.

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  2. Show that (a sin x + b cos x)/(a cos x - b sin x) increases with x.

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  3. Find the stationary points and stationary values for the following fun...

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  4. Find the stationary points and stationary values for the following fun...

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  5. Find the stationary points and stationary values for the following fun...

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  6. Find the stationary points and stationary values for the following fun...

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  7. The turning values of x^3-3px+q(p gt 0) are

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  8. Find the maximum or minimum values of the following functions. 4x - ...

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  9. Find the maximum or minimum values of the following functions. x + ...

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  10. Find the maximum or minimum values of the following functions. x^(3...

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  11. For what values of k, f(x) = x-(k)/(x) has a maximum value at x = -2.

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  12. If y = sum(i=1)^(n)(x-x(i))^(2), x(i) are constants, then for what val...

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  13. If xy(y-x) = 2a^(3), show that y has a minimum value when x = a.

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  14. Show that the least value of a^(2) sec^(2)x + b^(2) "cosec"^(2)x is (...

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  15. If x, y, k, m, n are positive and x + y = k, then find the maximum val...

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  16. Find the greatest and least value of (sin x)^((sin x)).

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  17. If x, y are positive real numbers such that xy = 1 then show that the ...

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  18. If the sum fo two positive numbers is 20 then show that the maximum va...

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  19. If the sum of two positive numbers is 48 then find the two numbers who...

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  20. The sum of two numbers is 20 . If the product of the square of one num...

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