Evaluate the following Limits: limx→3[x-3x-2-4-x] - Mathematics and Statistics

Evaluate the following Limits: `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`

बेरीज

`lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`

= `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x)) xx(sqrt(x - 2) + sqrt(4 - x))/(sqrt(x - 2) + sqrt(4 - x))]`

= `lim_(x ->3) ((x - 3)(sqrt(x - 2) + sqrt(4 - x)))/((x - 2) - (4 - x)`

= `lim_(x -> 3) ((x - 3)(sqrt(x - 2) + sqrt(4 - x)))/(2x - 6)`

= `lim_(x -> 3) ((x - 3)(sqrt(x - 2) + sqrt(4 - x)))/(2(x - 3)`

= `lim_(x -> 3) (sqrt(x - 2) + sqrt(4 - x))/2 ...[("As" x -> 3"," x ≠ 3),(therefore x - 3 ≠ 0)]`

= `1/2 lim_(x -> 3)(sqrt(x - 2) + sqrt(4 - x))`

= `1/2(sqrt(3 - 2) + sqrt(4 - 3))`

= `1/2(1 + 1)`

= 1

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पाठ 7: Limits - MISCELLANEOUS EXERCISE - 7 [पृष्ठ १०६]

पाठ 7 Limits
MISCELLANEOUS EXERCISE - 7 | Q II. 5) | पृष्ठ १०६

Evaluate the following limits: `lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]`

Evaluate the following limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`

Evaluate the following limits: `lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`

Evaluate the following limit :

`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`

Evaluate the following limit :

`lim_(u -> 1) [(u^4 - 1)/(u^3 - 1)]`

Evaluate the following limit :

`lim_(Deltax -> 0) [((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)]`

Evaluate the following limit :

`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`