In exercise problems 7 - 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why? limx→3(4-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 -> 3) (4 - x)`

Graph

From the graph the value of the function at x = 3 is y = f(3) = 1

∴ `lim_(x -> 3) (4 - x)` = 1

shaalaa.com

Is there an error in this question or solution?

Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [Page 96]

Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 7 | Page 96

Evaluate the following limit :

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

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

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

In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> - 3) (sqrt(1 - x) - 2)/(x + 3)`

x	– 3.1	– 3.01	– 3.00	– 2.999	– 2.99	– 2.9
f(x)	– 0.24845	– 0.24984	– 0.24998	– 0.25001	– 0.25015	– 0.25158

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`

Sketch the graph of f, then identify the values of x₀ for which `lim_(x -> x_0)` f(x) exists.

f(x) = `{{:(x^2",", x ≤ 2),(8 - 2x",", 2 < x < 4),(4",", x ≥ 4):}`

Sketch the graph of a function f that satisfies the given value:

f(0) is undefined

`lim_(x -> 0) f(x)` = 4

f(2) = 6

`lim_(x -> 2) f(x)` = 3

Evaluate : `lim_(x -> 3) (x^2 - 9)/(x - 3)` if it exists by finding `f(3^-)` and `f(3^+)`