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

Sum

`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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Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [Page 98]

Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 19 | Page 98

Evaluate the following limit:

`lim_(y -> -3) [(y^5 + 243)/(y^3 + 27)]`

Evaluate the following limit :

`lim_(x -> 0)[(root(3)(1 + x) - sqrt(1 + x))/x]`

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 -> 5) |x - 5|/(x - 5)`

Verify the existence of `lim_(x -> 1) f(x)`, where `f(x) = {{:((|x - 1|)/(x - 1)",", "for" x ≠ 1),(0",", "for" x = 1):}`

Evaluate the following limits:

`lim_(x - 0) (sqrt(1 + x^2) - 1)/x`

Find the left and right limits of f(x) = `(x^2 - 4)/((x^2 + 4x+ 4)(x + 3))` at x = – 2

Find the left and right limits of f(x) = tan x at x = `pi/2`

Evaluate the following limits:

`lim_(x -> oo) ((2x^2 + 3)/(2x^2 + 5))^(8x^2 + 3)`

Evaluate the following limits:

`lim_(x -> 0) (sqrt(1 + sinx) - sqrt(1 - sinx))/tanx`

Evaluate the following limits:

`lim_(x -> 0) ("e"^("a"x) - "e"^("b"x))/x`