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Let L(1)=lim(xrarr4) (x-6)^(x)and L(2)=l...

Let `L_(1)=lim_(xrarr4) (x-6)^(x)and L_(2)=lim_(xrarr4) (x-6)^(4)`.
Which of the following is true?

A

Both `L_(1) and L_(2)` exists

B

Neither `L_(1)` nor `L_(2)` exists

C

`L_(1)` exists but `L_(2)` does not exist

D

`L_(2)` exists but `L_(1)` does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
If `("variable")^("variable")` and base is negative then limit does not exist. And `underset(xrarr4)(lim)(x-6)^(4)=16`.
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CENGAGE-LIMITS-Single Correct Answer Type
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  2. Which of the following limits exists finitely?

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  3. Let L(1)=lim(xrarr4) (x-6)^(x)and L(2)=lim(xrarr4) (x-6)^(4). Which ...

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  4. Set of all values of x such that lim(nrarroo) (1)/(1+((4tan^(-1)(2pix)...

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  5. lim(xrarroo) [x-log(e)((e^(x)+e^(-x))/(2))]=

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  6. lim(xrarroo) {(e^(x)+pi^(x))^((1)/(x))}= (where {.} denotes the fracti...

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  7. If (cos x)/(sin ax) is periodic function, then lim(mrarroo)(1+cos^(2...

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  8. The value of lim(xrarr0) (sqrt(1-cosx^(2)))/(1-cos x) is

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  9. lim(xrarr(pi)/(2)) (1-sinx)tanx=

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  10. The value of lim(xrarroo) x^(2)(1-cos.(1)/(x)) is

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  11. lim(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

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  12. lim(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  13. underset(xrarr2^(+))(lim){x}(sin(x-2))/((x-2)^(2))= (where {.} denotes...

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  14. lim(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)}...

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  15. lim(xrarr0) (3 tan3x-4 tan2x-tanx)/(4x^(2)tanx)

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  16. lim(xrarr0) [(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest...

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  17. The value of lim(xrarr(pi)/(4)) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

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  18. The value of lim(xrarroo) (e^(sqrt(x^(4)+))-e^((x^(2)+1))) is

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  19. The value of lim(xrarrpi//4) (tan^(3)x-tanx)/(cos(x+(pi)/(4))) is

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  20. lim(xrarr(pi)/(2)) ((1-sinx)(8x^(3)-pi^(3))(cosx))/(pi-2x)^(4)

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