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Prove that the function f(x) = tan x -4x...

Prove that the function `f(x) = tan x -4x` is strictly decreasing on `(- (pi)/(3), (pi)/(3))`.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION B (60 MARKS)
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  2. Find the equations of all the lines of slope 2 and that are tangent to...

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  3. Prove that the function f(x) = tan x -4x is strictly decreasing on (- ...

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  4. If y= cos^(-1) { 2x sqrt(1-x^(2) ) } , find (dy)/(dx).

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  5. If y = ( sin y )^(x), find (dy)/(dx).

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  6. Verify Rolle.s theorem for f(x) = (sin x)/( e^(x)) on 0 le x le pi.

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  7. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

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  8. Solve (x+1) (dy)/(dx) = 2xy.

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  9. Evaluate int e^(x) ((1- sin x)/( 1- cos x) ) dx

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  10. Find the area of the region bounded by the curve y=x^(3) and the lines...

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  11. Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 ...

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  12. Find the vector equation of the plane passing through the points 3 hat...

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  13. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  14. Find the equation in vector and Cartesian from of the plane passing th...

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  15. Prove that sin( cos^(-1) ""(3)/(5) + sin^(-1)""(5)/(13) ) = (63)/(65)

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  16. Answer any three questions (b) A house wife wishes to mix together t...

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  17. Answer any three questions (c) Show that f: [-1,1] to R, given by f(...

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  18. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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  19. Answer any three questions (e) If a gt b gt c gt0, then prove that c...

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  20. A bag contains 6 black and 3 white balls. Another bag contains 5 black...

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