In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why? limx→x2tanx

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`

Graph

`lim_(x -> x/2) tan x`

y = f(x) = sec x

From the graph at x = `pi/2`, the curve does not intersect the line x = `pi/2`

At x = `pi/2`, he value of the function y = f(x) does not exist.

Hence `lim_(x -> x/2) tan x` does not exist.

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Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [Page 97]

Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 15 | Page 97

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 -> 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 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 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 -> 3) 1/(x - 3)`

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

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