Solution of Quiz2 STA 301

Question # 1 of 10 ( Start time: 03:43:28 PM ) Total Marks: 1

If the function f(x)= (x^2)+1 satisfies all the conditions of Rolle’s theorem in the interval [-1,1] , then the value of ‘c’ will be……..

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0

2

3

4

Question # 2 of 10 ( Start time: 03:44:36 PM ) Total Marks: 1

‘x.ln(x/e)’ is the anti-derivative of ‘lnx’ if and only if the derivative of ‘x.ln(x/e)’ is euqal to --------

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x

xln(x/e)

lnx

ln(x/e)

Question # 3 of 10 ( Start time: 03:45:24 PM ) Total Marks: 1

Integral of (5/2)cos(x) is

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(3/2)csc(x)+C                    

(5/2)tan(x)+C

(5/2)sin(x)+C                     

None of these

Question # 4 of 10 ( Start time: 03:45:45 PM ) Total Marks: 1

summation of (n+i) ; (i varies from 1 to 10 ) , here ‘i’ is known as the …….. of the summation.

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Index 

Lower limit

Upper limit

None of these

   

Question # 5 of 10 ( Start time: 03:46:13 PM ) Total Marks: 1

The estimated area under f(x) = x^2 + 2 from x = 1 to x = 5 with right end points for n = 2 is ________.

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30.

28.

50.

76. 

   

Question # 6 of 10 ( Start time: 03:46:53 PM ) Total Marks: 1

(1^3)+(2^3)+(3^3)+….+(20^3) equals --------- NOTE: x^n means ‘x’ to the power ‘n’

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42925  

34548

44100

None of these      

   

Question # 7 of 10 ( Start time: 03:47:40 PM ) Total Marks: 1

If the definite integral of f(x)=3 over [1,x] is greater than ‘12’ then -----

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x>12

x>5

x>3

x>1

Question # 8 of 10 ( Start time: 03:48:15 PM ) Total Marks: 1

x=1 is a critical value of the function. f(x)=(x-1)^3 NOTE: x^n means ‘x’ to the power ‘n’

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False

 True                                       

Question # 9 of 10 ( Start time: 03:48:42 PM ) Total Marks: 1

If f(x) =cos(x) then mean value theorem can be applied on this in the interval (pi/2, 3pi/2)

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True                                       

False

Question # 10 of 10 ( Start time: 03:49:00 PM ) Total Marks: 1

If x =(1+2+3+...+10)+{(1^3)+(2^3)+(3^3)+...+ (10^3)}, then x = _______.

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110. 

55.

3025.

3080.