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Q. For every integer n, leta(n) and b(n...

Q. For every integer n, let`a_(n)` and `b_(n)` be real numbers. Let function `f:R->R` be given by a `f(x)={{:(a_n+sin pix, for x in [2n,2n+1]), (b_n+cos pix, for x in (2n+1,2n)):}` for all integers n.

A

`a_(n-1) - b_(n-1) = 0`

B

`a_(n) - b_(n) = 1`

C

`a_(n) - b_(n+1) = 1`

D

`a_(n-1) -b_(n) = -1`

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

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  3. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  4. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

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  5. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

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  6. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  10. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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  11. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

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  12. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

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  13. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

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  14. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  15. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

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  16. Which of the following functions is differentiable at x = 0 ?

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  17. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

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  18. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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  19. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  20. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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