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The value of lim( x to 3) (x^(5)-3^(5))/...

The value of `lim_( x to 3) (x^(5)-3^(5))/(x^(8)-3^(8))` is equal to

A

`(5)/(8)`

B

`(5)/(64)`

C

`(5)/(216)`

D

`(1)/(27)`

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 3) (x^(5)-3^(5))/(x^(8)-3^(8))=lim_(x to 3)(5x^(4))/(8x^(7)) " "[(0)/(0)"form"]`
`" " `[by L' Hospital's rule]
`=lim_(x to 3) (5)/(8x^(3))=(5)/(8xx3^(3))=(5)/(8xx27)=(5)/(216)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If lim(x to 1) (ax^(2)+bx+c)/((x-1)^(2))=2, then (a, b, c) is

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  2. lim(m to oo)("cos"(x)/(m))^(m) is equal to

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  3. The value of lim( x to 3) (x^(5)-3^(5))/(x^(8)-3^(8)) is equal to

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  4. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

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  5. At x=3, f(x) ={(x^(5)-243",", "if " x ne 3),(x^(3)-27",", "if " x=3):}...

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  6. The value of f(0), if f(x)=(x tan 2x)/(sin3x sin5x) is continuous at ...

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  7. f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...

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  8. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

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  9. The function f(x)=(x^3+x^2-16 x+20)/(x-2) is not defined for x=2. In o...

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  10. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, t...

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  11. if f(x) is continuous and f(9/2)=2/9 then the value if lim(x->0)f((1-c...

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  12. If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...

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  13. If f(x)={((1+2x)^(1//x)",","for " x ne 0),(e^(2)",", "for " x =0):}, t...

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  14. If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...

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  15. If f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):} then f(x) is

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  16. For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...

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  17. If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)...

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  18. Which of the following functions is continuous at x = 0 ?

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

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  20. For what value of k, f(x)={((2^(x+2)-16)/(4^(x)-16)",", x ne 2),(k",",...

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