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This mock test of Test: Limits And Continuity : Intuitive Approach - 3 for CA Foundation helps you for every CA Foundation entrance exam.
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QUESTION: 1

If f(x) = (x^{2 }-4)÷(x-2) for x<2, f(x)=4 for x=2 and f(x)=2 for x>2, then f(x) at x = 2 is

Solution:

QUESTION: 2

f(x) = when x^{ o }0, then f(x) is

Solution:

QUESTION: 3

If = i, then which of the following is correct?

Solution:

QUESTION: 4

is equal to

Solution:

QUESTION: 5

If f(x) = x for 0 ≤ x 1/2, f(x) = 1 for x = 1-x for 1/2<x<1 then at x =1/2 the function is

Solution:

QUESTION: 6

e^{-1/x}[1+e^{1/x}]^{-1} is

Solution:

QUESTION: 7

If f(x)=9x÷(x+2) for x<1, f(1)=3, f(x)=(x+3)x-1 for x>1, then in the interval (-3,3) the function is

Solution:

QUESTION: 8

Solution:

QUESTION: 9

Function f(x) = K.x-1 for x < 2

= x-k for x ≥ 2

is continuous at x = 2

The value of 'k' is __________.

Solution:

QUESTION: 10

Solution:

QUESTION: 11

Evaluate

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QUESTION: 12

Evaluate

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QUESTION: 13

The points of discontinuity of the function, F(x) = are

Solution:

QUESTION: 14

Solution:

QUESTION: 15

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QUESTION: 16

Find limn→∞(2n-1)2^{n }(2n+1)^{-1} 2^{1-n}

Solution:

QUESTION: 17

Find lim_{n→∞}[4n^{2} + 6n +2] ÷ 4n^{2}

Solution:

QUESTION: 18

Find lim_{n→∞}[x^{n}.(n+1)] ÷ [nx ^{n+1} ]

Solution:

QUESTION: 19

Find lim_{n→∞}[n(n+2)] ÷ (n+1)^{2}

Solution:

QUESTION: 20

Find lim_{n→∞}(n^{3} +a )[(n+1)^{3}a]^{-1} (2^{n+1} +a ) (2^{n} +a)^{-1}

Solution:

QUESTION: 21

Find lim_{n→∞}(n^{2} +1)[(n+1)^{2} +1]^{-1} 5^{n+1} 5^{-n}

Solution:

QUESTION: 22

Find lim_{n→∞}n^{n}(n+1)^{-n-1} ÷ n^{-1}

Solution:

QUESTION: 23

Find lim_{n→∞}2^{n-1} (10 +n) (9+n)^{-1} 2^{-n}

Solution:

QUESTION: 24

Find lim_{n→∞}(1+n^{-1})[1+2n)^{-1}]^{-1}

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QUESTION: 25

Find lim_{n→∞}[n^{n}. (n+1)!] ÷ [n! (n+1)^{n+1}]

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QUESTION: 26

Find lim_{n→∞}[(n+1)^{n+1}. n^{-n-1} -(n+1).n^{-1}]^{-n}

Solution:

QUESTION: 27

3x^{2}+2x-1 is continuous

Solution:

QUESTION: 28

Find lim_{n→∞}n^{n} (1+n)^{-n}

Solution:

QUESTION: 29

Find lim_{n→∞}[n!3^{n+1}] ÷[3^{n}(n+1)!]

Solution:

QUESTION: 30

The value of the limit when x tends to zero of the expression (1+n)^{1/n} is

Solution:

QUESTION: 31

The value of the limit when x tends to zero of the expression (1+n)^{1/n} is

Solution:

QUESTION: 32

The value of the limit when x tends to zero of the expression [(1+x)^{n}-1] ]

Solution:

QUESTION: 33

The value of the limit when x tends to 2 of the expression (x-2)^{-1}-(x^{2}-3x+2)^{-1} is

Solution:

QUESTION: 34

The value of the limit when x tends to zero of the expression (e^{x}-1)/x is

Solution:

QUESTION: 35

The value of the limit when n tends to infinity of the expression 2^{-n}(n^{2}+5n+6)[(n+4)(n+5)]^{-1} is

Solution:

QUESTION: 36

The value of the limit when x tends to zero of the expression (1+n)^{1/n} is

Solution:

QUESTION: 37

Find lim_{n→∞}[n^{1/2} + (n+1)^{1/2}]^{-1} ÷ n^{-1/2 }

Solution:

QUESTION: 38

The value of the limit when x tends to zero of the expression [(a+x^{2})^{1/2}

Solution:

QUESTION: 39

Find lim_{n→∞} (2^{n}-2)(2^{n}+1)^{-1}

Solution:

QUESTION: 40

Find lim_{n→∞} [(n^{3} +1)^{1/2 }- n ^{3/2] ÷ n3/2 }

Solution:

### PPT - Limits & Continuity (Part - 3)

Doc | 43 Pages

### Limits & Continuity Worksheet

Doc | 3 Pages

- Test: Limits And Continuity : Intuitive Approach - 3
Test | 40 questions | 40 min

- Test: Limits And Continuity : Intuitive Approach - 2
Test | 40 questions | 40 min

- Test: Limits And Continuity : Intuitive Approach - 1
Test | 40 questions | 40 min

- Test: Continuity
Test | 10 questions | 10 min

- Test: Probability Experimental Approach
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