Find the left and right limits of f(x) = tan x at x = π2 - Mathematics

Find the left and right limits of f(x) = tan x at x = `pi/2`

Sum

To find the left limit of f(x) at x = `pi/2`

Put x = `pi/2 - "h"`

Whee h > 0

When `x -> pi/2`

We have h → 0

`lim_(x -> pi^-/2) (tan x) = lim_("h" -> 0) tan(pi/2 - "h")`

= `lim_("h" -> 0) cot "h"`

= cot (0)

= `oo`

`lim_(x -> pi^-/2) (tan x) = oo`

To find the right limit of f(x) at x = `pi/2`

Put x = `pi/2 + "h"`

Whee h > 0

When `x -> pi/2`

We have h → 0

`lim_(x -> pi^+/2) (tan x) = lim_("h" -> 0) tan(pi/2 + "h")`

= `lim_("h" -> 0) (- cot"h")`

= `- lim_("h" -> 0) cot "h"`

`lim_(x -> pi^+/2) (tan x)` = – cot 0

= `- oo`

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Concept of Limits

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Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.3 [Page 111]

Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.3 | Q 1. (b) | Page 111

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