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Relations And Functions

Question
CBSEENMA12036190
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The function f: R ~ {0} → R given by
straight f left parenthesis straight x right parenthesis space equals space 1 over straight x minus fraction numerator 2 over denominator straight e to the power of 2 straight x end exponent minus 1 end fraction
can be made continuous at x = 0 by defining f(0) as

  • 2

  • -1

  • 1

  • 0

Solution

C.

1

limit as straight x rightwards arrow 0 of space 1 over straight x space minus fraction numerator 2 over denominator straight e to the power of 2 straight x end exponent minus 1 end fraction limit as straight x rightwards arrow 0 of space fraction numerator straight e to the power of 2 straight x end exponent minus 1 minus 2 straight x over denominator straight x left parenthesis straight e to the power of 2 straight x end exponent minus 1 right parenthesis end fraction limit as straight x space rightwards arrow 0 of space fraction numerator 2 straight e to the power of 2 straight x end exponent minus 2 over denominator left parenthesis straight e to the power of 2 straight x end exponent minus 1 right parenthesis plus 2 xe to the power of 2 straight x end exponent end fraction limit as straight x rightwards arrow 0 of space space fraction numerator 4 straight e to the power of 2 straight x end exponent over denominator 4 straight e to the power of 2 straight x end exponent space plus 4 xe to the power of 2 straight x end exponent end fraction space equals space 1

Some More Questions From Relations and Functions Chapter

If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

lf a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.

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