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Let [x] denotes the greatest integer les...

Let [x] denotes the greatest integer less than or equal to x. If `f(x) =[x sin pi x]`, then `f(x)` is

A

a. continuous at x=0

B

b. continuous in (-1,0)

C

c. differentiable at x=1

D

d. differentiable in (-1,1)

Text Solution

Verified by Experts


From the graph, `0 le x sin pix lt 1`, for `x in [-1, 1]`
Hence `f(x) = 0, AA x in [-1, 1]`
Thus, correct answers are (a), (b) and (d).
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CENGAGE PUBLICATION-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercises
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  3. Draw the graph of y = cos pix.

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  4. Draw the graph of y = cos^(2)x.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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