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Show that 2sinx+tanxge3x for all x epsil...

Show that 2sinx+tanx`ge`3x for all x `epsilon(0,(pi)/(2))`.

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The correct Answer is:
`2sinx+3tanxgt3x`
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ARIHANT PUBLICATION-CHSE ODISHA EXAMINATION PAPER - 2018 -SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)
  1. Prove that |[a-b-c,2a,2a],[2b, b-c-a, 2b],[2c, 2c, c-a-b]|= (a+b+c)^3.

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  2. Show that the sum of the intercepts on the coordinate axes of any tang...

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  3. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  4. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  5. Differentiate y=(siny)^(sin2x)

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  6. Test the continuity of the following function at x=0 f(x)={{:((1-e^(...

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  7. From the differential equation whose general solution is y=asint+be^t.

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  8. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  9. Evaluate int (dx)/((x+1)sqrt(1-x^2))

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  10. int(0)^(1/2)(1)/(sqrt(1-x^(2)))dx.

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  11. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  12. Prove that the measure of the angle between two main diagonals of a cu...

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  13. The position vectors of two points A and B are 3hati+hatj+2hatk and ha...

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  14. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  15. Prove that [(veca+vecb,vecb+vecc,vecc+veca)]=2[(veca,vecb,vecc)].

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  16. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  17. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  18. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

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  19. Solve the following LPP graphically : Maximize Z=3x(1) +2x(2) subj...

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  20. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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