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For f(x) = sin x - x^(2) + 1, check weat...

For `f(x) = sin x - x^(2) + 1`, check weather the function is increasing, decreasing or has a point of extremum ?

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`f(x) = sin x - x^(2) + 1`
`therefore` `f'(x) = cos x - 2x`
Now draw the graphs of y = cos x and y = 2x.

From the graph, for `x lt x_(0), cos x gt 2x rArr f'(x) gt 0`
`x gt x_(0), cos x lt 2x rArr f'(x) lt 0`
Hence `x = x_(0)` is the point of maxima.
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CENGAGE PUBLICATION-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercises
  1. Draw the graph of y = cos^(2)x.

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  2. Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0...

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  3. Draw the graph of y = tan^(2) x.

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  4. Draw the graph of y = sin x + cos x, x in [0, 2pi].

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  5. Draw the graph of y = [cos x], x in [0, 2pi], where [*] represents the...

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  6. Draw the graph of y = sin pisqrt(x).

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  7. The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is ...

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  8. Evaluate : [lim(x to 0) (tan x)/(x)], where [*] represents the greates...

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  9. For f(x) = sin x - x^(2) + 1, check weather the function is increasing...

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  10. Draw the graph of the function f(x)=m a x{sinx ,cos2x},x in [0,2pi]. W...

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  11. Draw the graph of [y] = sin x, x in [0,2pi] where [*] denotes the grea...

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  12. The total number of solution of sin{x}=cos{x} (where {} denotes the fr...

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  13. Draw the graph of f(x) = |sinx| + |cos x|, x in R.

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  14. Find the number of solutions to cos x = (x)/(10), x gt 0.

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  15. The number of solutions of tanx-m x=0,m >1, in (-pi/2,pi/2) is 1 (b) 2...

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  16. Find the number of solutions to log(e) |sin x| = -x^(2) + 2x in [-(pi)...

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  17. Solve : Cos x le - (1)/(2).

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  18. Prove that the least positive value of x , satisfying tanx=x+1,lies i...

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  19. Draw the graph of y = (x^(2))/(10) sin x.

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  20. Draw the graph of y = (sin x)/(x).

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