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Prove that f(x)=x/(sinx) is an inc...

Prove that `f(x)=x/(sinx)` is an increasing function while `g(x)=x/(tanx)` is decreasing function, where `0

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
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  2. Let f(x) be a increasing function defined on (0,\ oo)dot If f...

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  3. Prove that f(x)=x/(sinx) is an increasing function while g(x)=x/...

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  4. Let f(x)=x^3+2x^2+x+5. Show that f(x)=0 has only one real roo...

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  5. Prove that ln (1+1/x) gt (1)/(1+x), x gt 0. Hence, show that the fun...

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  6. For what values of a , does the function f(x)=((sqrt(a+5))/(1-a)...

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  7. The minimum value of the function f(x)=x^(3//2)+x^(-3//2)-4(x+1/x) ...

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  8. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

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  9. f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) su...

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  10. f(x) and g(x) are differentiable functions for 0 <= x <= 2 such that f...

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  11. Consider the function f(x)={xsinpi/x ,forx >0 0,forx=0 The, the numb...

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  12. The function f(x)=(log(pi+x))/(log(e+x))s is

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  13. The length of the longest interval in which the function 3sinx-4sin^3x...

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  14. Using the relation 2(1-cosx)<x^2,x!=0 or otherwise, prove that s in(t ...

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

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  16. If f(x)={(x^(alpha)logx , x > 0),(0, x=0):} and Rolle's theorem is ap...

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  17. If f(x) is differentiable and strictly increasing function, then the v...

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  18. Using Rolles theorem, prove that there is at least one root in (45^(1/...

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  19. Let f(x) be a twice differentiable function for all real values of x a...

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  20. let f(x)=2+cosx for all real x Statement 1: For each real t, there ex...

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