In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why? limx→1f(x) where ,,f(x)={x2+2,x≠11,x=1 - 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 -> 1) f(x)` where `f(x) = {{:(x^2 + 2",", x ≠ 1),(1",", x = 1):}`

Graph

`f(x) = {{:(x^2 + 2",", x ≠ 1),(1",", x = 1):}`

To find `lim_(x -> 1) f(x)`

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

∴ `lim_(x -> 1) f(x)` = 3

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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 10 | Page 96

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

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):}`

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 -> x/2) tan x`

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

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

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