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Find the number of solutions of the equa...

Find the number of solutions of the equation `3tanx+x^3=2 when x in (0,pi/4)`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

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  2. Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,...

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  3. Find the number of solutions of the equation 3tanx+x^3=2 when x in...

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  4. If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have a....

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  5. Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of...

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  6. If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...

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  7. Show that tan^(-1)x > x/(1+(x^2)/3)ifx in (0,oo)dot

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  8. Consider the function f(x)={xsinpi/x ,forx >0 ,forx=0 The number of ...

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  9. For x > 0 lf x=pi/2, show that x-(x^3)/6 < sinx < x

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

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  11. Show that 0 < xsinx-1/2 sin^2x < ((pi-1))/2 ,AAx in (0,pi/2) dot

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  12. The value of c in Lagranges theorem for the function f(x)=logsinx in t...

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  13. Prove that ln(1+x) < x for x > 0.

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  14. If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles...

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  15. Prove that |cosalpha-cosbeta|lt=|alpha-beta|

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  16. A value of 'c' for which the conclusion of mean value theorem holds fo...

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  17. If a , b > 0 a n d 0 < p < 1, then prove that (a+b)^p < a^p+b^pdot

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  18. Each question has four choices, a,b,c and d, out of which only one is ...

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  19. Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...

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  20. The abscissa of the point on the curve sqrt(x y)=a+x the tangent at wh...

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