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Prove that the least positive value of x...

Prove that the least positive value of `x ,` satisfying `tanx=x+1,` lies in the interval `(pi/4,pi/2)`

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Let f(x) = tan x and g(x) = x + 1, which could be shown as follows.

From the above the figure, tan x = x + 1 has infinitely many solutions, but the least positive value of `x in ((pi)/(4), (pi)/(2)).`
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CENGAGE ENGLISH-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. Find the number of roots of the equation x sin x = 1, x in [-2pi, 0) ...

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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 xdot{sinx ,cos2x},x in [0,2pi]...

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

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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) = |tan x| + |cot x|.

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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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