Write a brief description of the meaning of the notation limx→8f(x) = 25

Write a brief description of the meaning of the notation `lim_(x -> 8) f(x)` = 25

बेरीज

`lim_(x -> 8) f(x)` = 25

`lim_(x -> 8^-) f(x)` = 25

`lim_(x -> 8^+) f(x)` = 25

`lim_(x -< 8^-) f(x) = lim_(x ->8^+) f(x)`

`f(8^-) = f(8^+)` = 25

(i.e.) `lim_(x -> 8) f(x)` = 25

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पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [पृष्ठ ९८]

पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 19 | पृष्ठ ९८

Evaluate the following limit:

`lim_(x -> 5)[(x^3 - 125)/(x^5 - 3125)]`

Evaluate the following limit :

`lim_(z -> "a")[((z + 2)^(3/2) - ("a" + 2)^(3/2))/(z - "a")]`

Evaluate the following :

`lim_(x -> 0) [(sqrt(1 - cosx))/x]`

Evaluate the following :

`lim_(x -> 0) {1/x^12 [1 - cos(x^2/2) - cos(x^4/4) + cos(x^2/2) cos(x^4/4)]}`

In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> 0) sin x/x`

x	– 0.1	– 0.01	– 0.001	0.001	0.01	0.1
f(x)	0.99833	0.99998	0.99999	0.99999	0.99998	0.99833

In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?

`lim_(x -> 2) f(x)` where `f(x) = {{:(4 - x",", x ≠ 2),(0",", x = 2):}`