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if f(x) is continuous and f(9/2)=2/9 the...

if `f(x)` is continuous and `f(9/2)=2/9` then the value if `lim_(x->0)f((1-cos3x)/x^2)`is

A

`(2)/(9)`

B

`(9)/(2)`

C

18

D

81

Text Solution

Verified by Experts

The correct Answer is:
A
Now, `lim_(x to 0) f((1-cos 3x)/(x^(2)))=f(lim_(x to 0) (1-cos 3x)/(x^(2)))`
`=f(lim_(x to 0) +(3 sin 3x)/(2x))`
`=f(lim_( x to 0) (9 cos 3x)/(2))=f((9)/(2))`
`=(2)/(9) " " [ because f((9)/(2))=(2)/(9) "given"]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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  10. Which of the following functions is continuous at x = 0 ?

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  11. For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...

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  13. For what value of k, the function f(x)={((x)/(|x|+2x^(2))",", x ne 0)...

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  14. The points of discontinuity of the function lim(n->oo) (((2 sin x )^(2...

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  15. The function f(x)=(sin 2x)^(tan^(2)2x) is not defined at x=(pi)/(4). T...

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  16. If the function f as defined below is continuous at x=0find the values...

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  17. If a function y=f(x) is defined as y=(1)/(t^(2)-t-6)and t=(1)/(x-2), t...

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  18. Let f(x)={((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2)"," , x ne 0),(a",",...

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  19. Let f(x)={(1-cos4x)/(x^2),\ \ \ if\ x<0a ,\ \ \ if\ x=0(sqrt(x))/(sqrt...

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