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

योग

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

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

Evaluate the following limit :

`lim_(x -> 0)[((1 - x)^8 - 1)/((1 - x)^2 - 1)]`

Evaluate the following limit :

`lim_(y -> 1)[(2y - 2)/(root(3)(7 + y) - 2)]`

In the following example, given ∈ > 0, find a δ > 0 such that whenever, |x – a| < δ, we must have |f(x) – l| < ∈.

`lim_(x -> 1) (x^2 + x + 1)` = 3

Evaluate the following :

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

In problems 1 – 6, using the table estimate the value of the limit.

`lim_(x -> 2) (x - 2)/(x^2 - x - 2)`

x	1.9	1.99	1.999	2.001	2.01	2.1
f(x)	0.344820	0.33444	0.33344	0.333222	0.33222	0.332258

In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> 2) (x - 2)/(x^2 - 4)`

x	1.9	1.99	1.999	2.001	2.01	2.1
f(x)	0.25641	0.25062	0.250062	0.24993	0.24937	0.24390

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 -> 1) sin pi x`

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 -> 0) sec x`

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning