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 - Mathematics

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 :

If `lim_(x -> 5) [(x^"k" - 5^"k")/(x - 5)]` = 500, find all possible values of k.

Evaluate the following limit :

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

Evaluate the following limit :

`lim_(x -> 1) [(x + x^3 + x^5 + ... + x^(2"n" - 1) - "n")/(x - 1)]`

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 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 -> 3) (4 - x)`

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