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Thought-Process to Discover Knowledge

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figure-out, &
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User Guide

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

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User Guide

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User Guide

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User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Calculating Limits

Voice

Voice

Home

Limit of Functions with Indeterminate Value

»  A function f(x) at x=a is
→  not defined: if LHL != RHL and f(a) !in RR

### Limit of Functions with indeterminate values

plain and simple summary

nub

plain and simple summary

nub

dummy

If a function does not have value in real numbers and the two limits are not equal then the function is indeterminate at that input value.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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With an example, calculation of limits for an indeterminate function is discussed. The condition under which a function is indeterminate is illustrated with an example.

Keep tapping on the content to continue learning.
Starting on learning "limit of functions with indeterminate values". ;; With an example, calculation of limits for an indeterminate function is discussed. The condition under which a function is indeterminate is illustrated with an example.

Given function f(x)=tan x. what is f(x)|_(x=pi/2)?

• +oo
• -oo
• 0

The answer is '+oo'

f(pi/2)
quad quad = tan(pi/2)
quad quad = oo

Given function f(x)=tan x.what is left-hand-limit lim_(x->pi/2-)f(x)?

• +oo
• -oo
• 0

The answer is '+oo'

lim_(x->pi/2-)f(x)
quad quad = f(pi/2-delta)
quad quad = tan(pi/2-delta)
quad quad = (sin(pi/2-delta))/(cos(pi/2-delta))
quad quad = (cos(delta))/(sin(delta))
quad quad = 1/0
quad quad = oo

Given function f(x)=tan x.what is right-hand-limit lim_(x->pi/2+)f(x)?

• +oo
• -oo
• 0

The answer is '-oo'

lim_(x->pi/2+)f(x)
quad quad = f(pi/2+delta)
quad quad = tan(pi/2+delta)
quad quad = (sin(pi/2+delta))/(cos(pi/2+delta))
quad quad = (cos(delta))/(-sin(delta))
quad quad = -1/0
quad quad = -oo

Given function f(x)=tan x.

•  f(pi/2)=oo

•  lim_(x->pi/2-)f(x) = oo

•  lim_(x->pi/2+)f(x) = -oo
The function is not continuous and not defined at x=pi/2.

If the function evaluates to +-oo or 0/0 and the limits are not equal, then the function is not defined at that input value.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Function not Defined: If f(a) !in RR and lim_(x->a-)f(x) !=lim_(x->a+)f(x) then the function is not defined at x=a.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Examine the function f(x) = 1/(x-3) at x=3.

• Continuous
• defined
• not defined

Progress

Progress

Given function f of x = tan x. What is f of x at x = pi by 2?
plus
plus infinity
minus
minus infinity
0
0
The answer is "plus infinity" ;; f of pi by 2, equals tan pi by 2, equals infinity.
Given function f of x = tan x. What is left-hand-limit limit x tending to pi by 2 minus, f of x?
plus
plus infinity
minus
minus infinity
0
0
The answer is "plus infinity". ;; limit x tending to pi by 2 minus, f of x ;; equals f of pi by 2 minus delta ;; equals tan pi by 2 minus delta ;; equals sine pi by 2 minus delta divided by cos pi by 2 minus delta;; equals cos delta by sine delta ;; equals 1 by 0;; equals infinity
Given function f of x = tan x. What is right-hand-limit, limit x tending to pi by 2 +, f of x?
plus
plus infinity
minus
minus infinity
0
0
The answer is "minus infinity". ;; limit x tending to pi by 2 +, f of x ;; equals f of pi by 2 + delta ;; equals tan pi by 2 + delta ;; equals sine pi by 2 + delta divided by cos pi by 2 + delta;; equals cos delta by minus sine delta ;; equals minus 1 by 0;; equals minus infinity
Given function f of x = tan x. ;; f of pi by 2 = infinity ;; limit x tending to pi by 2 minus, f of x = infinity;; limit x tending to pi by 2 +, f of x = minus infinity ;; the function is not continuous and not defined at x = pi by 2.
If the function evaluates to plus or minus infinity or 0 by 0 and the limts are not equal, then the function is not defined at that input value.
If a function does not have value in real numbers and the two limits are not equal then the function is indeterminate at that input value.
function not defined: if f of a not in rel numbers, and limit x tending to a. minus f of x not equals limit x tending to a. plus f of x, then the function is not defined at x = a.
Examine the function f of x equals 1 by x minus 3 at x=3.
continuous
Continuous
defined
defined
not defined;not
not defined