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underset (x to 1) lim sqrt(1-cos 2(x-1))...

`underset (x to 1) lim sqrt(1-cos 2(x-1))/(x-1)`

A

exists and it equals `sqrt(2)`

B

exists and it equals `-sqrt(2)`

C

does not exist because `x-1 to 0`

D

does not exist because L.H.L is not equal to R.H.L.

Text Solution

Verified by Experts

The correct Answer is:
D
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. lim(x to 0)(sqrt((1/2)(1- cos 2x)))/x=

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  2. underset (x to 1) lim sqrt(1-cos 2(x-1))/(x-1)

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  3. If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):...

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  4. "lt"(x to infty) (log x)/[[x]], where [•] has the usual meaning is

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  5. The left hand limit of f(x) = {|x|^(3)/a -[x/a]^(3)}, (a gt 0) where...

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  6. lim(x rarr3)(|x-3|)/(x-3)=

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  7. Let f(x) = {{:(int(0)^(x) {5+|1-t|dt}, if x gt 2),(5x+1, if x le 2):},...

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  8. The value of lim(xto1^(+))(int(1)^(x)|t-1|dt)/(sin(x-1)) is

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  9. lim(x->a)(x)/(x-a)int(a)^(x)f(x)dx equals

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  10. If f(x) = {{:(x, x lt 0),(1, x=0),(x^(2), x gt a):}, then lim(x to 0) ...

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  11. If [x] denotes the greatest integer less than or equal to x,then the v...

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  12. Let f(x)={(x^2,x notin Z),((k(x^2-4))/(2-x),x notinZ):} Then, lim(xt...

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  13. If f(x)={:{(x,x le 1),(x^(2)+bx+c, x gt 1 and f'(x)) exists finitely f...

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  14. If f(x) is an odd function of x and "lt"(x to 0) f(x) exists then the...

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  15. Lt(x to 0)(e^(1//x)-1)/(e^(1//x)+1) is equal to:

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  16. lim(x to 0) (1+ sin x)^(1//x^(2)) is equal to:

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  17. lim(xto0)(sin[cosx])/(1+[cosx]), ([.] denotes the greatest integer fun...

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  18. The number of points at which the function f(x) = 1/(log|x|) is discon...

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  19. The function f(x) = (log(1+ax)-log(1-bx))/(x) is not defined at x = 0....

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  20. The value of f(0) so that the function f(x) = (log(1+x^(2) tanx)...

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