In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why? limx→2f(x) where ,,f(x)={4-x,x≠20,x=2

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):}`

Graph

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

To find `lim_(x -> 2) f(x)`

From the figure the value of the function at x = 2 is y = f(2) = 2

∴ `lim_(x -> 2) f(x)` = 2

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

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

Evaluate the following limit:

`lim_(z -> -3) [sqrt("z" + 6)/"z"]`

Evaluate the following limit:

`lim_(z -> -5)[((1/z + 1/5))/(z + 5)]`

Evaluate the following limit:

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

In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> 0) (sqrt(x + 3) - sqrt(3))/x`

x	– 0.1	– 0.01	– 0.001	0.001	0.01	0.1
f(x)	0.2911	0.2891	0.2886	0.2886	0.2885	0.28631

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

x	– 0.1	– 0.01	– 0.001	0.0001	0.01	0.1
f(x)	0.04995	0.0049999	0.0004999	– 0.0004999	– 0.004999	– 0.04995

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 a function f that satisfies the given value:

f(– 2) = 0

f(2) = 0

`lim_(x -> 2) f(x)` = 0

`lim_(x -> 2) f(x)` does not exist.