The limit of 1x1 + x - 1 + 1x2

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21.

The limit of 1x1 + x - 1 + 1x2 as x  0

  • does not exist

  • is equal to 12

  • is equal to 0

  • is equal to 1


B.

is equal to 12

limx01 + xx - 1 + 1x2= limx01 + x - 1 + x2x           00 form= limx0121 + x - x21 + x21       using l - Hospital rule= 121 +0 - 0= 12


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22.

The limit of xsine1x as x  0

  • is equal to 0

  • is equal to 1

  • is equal to e2

  • does not exist


23.

The limits of n = 11000- 1nxn as x  

  • does not exist

  • exists and equals to 0

  • exists and approaches to + 

  • exists and approaches to - 


24.

If f(x) = ex(x - 2)2, then

  • f is increasing in (- , 0) and (2, ) and decreasing in (0, 2).

  • f is increasing in (- , 0) and decreasing in (0, )

  • f is increasing in (2, ) and decreasing in (- , 0).

  • f is increasing in (0, 2) and decreasing in (- , 0) and (2, )


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25.

limx0πx - 11 + x - 1

  • does not exist

  • equals loge(π2)

  • equals 1

  • lies between 10 and 11


26.

The value of limn n!1nn

  • 1

  • 1e2

  • 12e

  • 1e


27.

The approximate value of 335 correct to 4 decimal places is

  • 2.0000

  • 2.1001

  • 2.0125

  • 2.0500


28.

The value of limnr = 1nr3r4 + n4 is

  • 12loge12

  • 14loge12

  • 14loge2

  • 12loge2


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29.

The value of limx1x + x2 + ... + xn - nx - 1

  • n

  • n + 12

  • nn + 12

  • nn - 12


30.

limx0sinπsin2xx2 is equal to

  • π2

  • 3π

  • 2π

  • π


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