Previous Years Gate Question | Calculus | Engineering Question | Limit question

Calculus

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Question no. 1

If f(x) = , then will be [2006 , marks 2]

looks_one -1/3

looks_two 5/18

looks_3 0

looks_4 2/5

Option looks_two 5/18

Solution :

Question no. 2

[ 2007 , marks 1 ]

looks_one 0.5

looks_two 1

looks_3 2

looks_4 undefined

option looks_one 0.5

Solution :

Question no. 3

What is the value of [ 2007 , marks 2 ]

looks_one 0

looks_two 1/6

looks_3 1/3

looks_4 1

Option looks_two 1/6

Solution :

Question no. 4

The value of : [ 2008 , 1 Mark ]

looks_one 1/16

looks_two 1/12

looks_3 1/8

looks_4 1/4

option looks_two 1/12

Solution :

Question no. 5

The value of : [2008 , 1 Mark]

looks_one 1

looks_two -1

looks_3 ∞

looks_4 -∞

Option looks_one 1

Solution :

Question no. 6

[2010 , Mark 1 ]

looks_one 2/3

looks_two 1

looks_3 3/2

looks_4 ∞

option looks_one 2/3

Solution :

Question no. 7

The value of [ 2010 , 1 mark]

looks_one 0

looks_two e^-2

looks_3 e^-1/2

looks_4 1

option looks_two e^-2

Solution :

Question no. 8

What is equal to ? [2011 , 1 Mark]

looks_one x

looks_two sin x

looks_3 0

looks_4 1

option looks_4 1

Solution :

Question no. 9

is : [2012 , 1 Mark]

looks_one 1/4

looks_two 1/2

looks_3 1

looks_4 2

Option looks_two 1/2

Solution :

Question no. 10

is equal to : [2013 , 1 Mark]

looks_one 0

looks_two 1

looks_3 ∞

looks_4 -1

Option looks_one 0

Solution :

Question no. 11

The value of [2014 , 1 mark]

looks_one ln 2

looks_two 1.0

looks_3 e

looks_4 ∞

Option looks_3 e

Solution :
Using the standard limit Formula :

Question no. 12

The value of : [ 2014 , 1 mark]

looks_one 0

looks_two 1

looks_3 3

looks_4 undefined

Option looks_one 0

Solution :

Question no. 13

equals to : [2014 , 1 Mark]

looks_one 0

looks_two 0.5

looks_3 1

looks_4 2

Option looks_two 0.5

Solution :

Question no. 14

[ 2014 , 1 mark ]

looks_one -∞

looks_two 0

looks_3 1

looks_4 ∞

Option looks_3 1

Solution :

Question no. 15

The expression is equal to : [2014 , marks 2 ]

looks_one log x

looks_two 0

looks_3 xlogx

looks_4 ∞

Option looks_one log x

Solution :
Using the limit formula

Question no. 16

The value of is [2015 , mark 1 ]

looks_one 0

looks_two 1/2

looks_3 1

looks_4 ∞

Option looks_4 ∞

Solution :
Given limit is in indeterminate form (0 / 0)
Apply L's Hospital

Question no. 17

The value of [ 2015 , mark 1 ]

looks_one -1

looks_two 1/3

looks_3 1

looks_4 -1/3

Option looks_4 -1/3

Solution :

Question no. 18

is equal to : [2015 , 1 Mark]

looks_one e^-2

looks_two e

looks_3 1

looks_4 e²

Option looks_4 e²

Solution :

Question no. 19

= [ 2016 , 1 mark ]

looks_one 0

looks_two 1

looks_3 -1

looks_4 Undefined

Option looks_two 1

Solution :

Question no. 20

is equal to : [ 2016 , 1 mark ]

looks_one 0

looks_two 1/12

looks_3 4/3

looks_4 1

Option looks_3 4/3

Solution :

Question no. 21

What is the value of [ 2016 , 1 mark ]

looks_one 1

looks_two -1

looks_3 0

looks_4 Undefined

Option looks_4 Undefined

Solution :

Question no. 22

is equal to : [ 2016 , 2 mark ]

looks_one 0

looks_two ∞

looks_3 1/2

looks_4 -∞

Option looks_3 1/2

Solution :
let x = 1/t

Question no. 23

= [ 2017 , 1 mark ]

looks_one 0

looks_two 3

looks_3 1

looks_4 -1

Option looks_4 -1

Solution :

Question no. 24

= [ 2017 , 1 mark ]

looks_one 0

looks_two 1

looks_3 -1

looks_4 Undefined

Option looks_3 -1

Solution :

Question no. 25

= [ 2017 , 2 mark ]

looks_one 0

looks_two -1

looks_3 1

looks_4 Undefined

Option looks_3 1

Solution :