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Lesson Posted on 04 Aug CBSE/Class 12/Science/Mathematics

Understanding Limits Through Graphs

Abhilash K S

Faculty for Engineering Mathematics in a private tuition center. Faculty for CAT/GMAT/GRE/SAT. Faculty...

Maths is often taught mechanically. Just consider the case of limits. Most of the standard textbooks define, the limit is the value that a function "approaches" as the input "approaches" some value. This neither gives the "feel" of maths, nor a beginner can appreciate its "beauty". A graphical approach... read more

Maths is often taught mechanically. Just consider the case of limits. Most of the standard textbooks define, the limit is the value that a function "approaches" as the input "approaches" some value.

This neither gives the "feel" of maths, nor a beginner can appreciate its "beauty". A graphical approach is often more insightful.

Consider, the graph of f(x)=1/x.

In this case, at X=0, the value of f(x) approaches minus infinity if we approach from the negative side of the number line and f(x) approaches plus infinity if we approach from the positive side of the number line. Essentially, the limit doesn't exist as LHL is minus infinity and RHL is plus infinity.

Now to make it more clear consider the graph of f(x)=1/x^2

Here at x=0, both LHL and RHL approaches plus infinity. Hence limit exists as plus infinity at x=0.

Just by observing these two graphs a beginner gets an insight into when a limit is said to exist and when not.

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Comments Answered on 04 Aug CBSE/Class 12/Science/Mathematics

Debesh Mukherjee

Mathematics & Statistics Teacher

Rs 300 per hour of Teaching/Coaching Mathematics which I usually charged for each student. = Debesh Mukherje

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Answers 5 Comments Answered on 19 Jul CBSE/Class 10/Mathematics/UNIT III: Coordinate Geometry/Coordinate geometry/Class 10 Difference between two points and section formula CBSE/Class 12/Science/Mathematics

How many solutions are there for

F(x)= 2^(x) - x-2

Ankita Das

Tutor

the number of solution is x

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Answers 1 Comments Looking for Class 12 Tuition

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Answered on 05 Aug CBSE/Class 10/Mathematics/UNIT III: Coordinate Geometry/Coordinate geometry/Class 10 Difference between two points and section formula CBSE/Class 12/Science/Mathematics

How many solutions are there for

F(x)= 2^(x) - x-2

Manu BK

Tutor

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Answers 2 Comments Lesson Posted on 05 Jul CBSE/Class 12/Science/Mathematics

Worksheet on Inverse trigo & Differentiation

Prateek Srivastava

I had completed my M-Tech and working as HOD Mathematics in a prestigious school of Noida as well as...

(CONCEPT BASED) Using principal value, find the value of cos^(-1) ? (cos ? ??(2 π)/3 ?? )+sin^(-1) ? (sin ? ??(2 π)/3 ?? ) Differentiate tan-1 w.r.t. x If e^x ??+e ??^y=e^(x+y), prove that dy/dx + e^(y-x)=0 Differentiate cos^(-1) ? ??((x+ √(1-x^2 ))/√2) ?? w.r.t. x If y √(x^2+1)=log... read more

(CONCEPT BASED)

Using principal value, find the value of cos^(-1)â?¡(cosâ?¡ã??(2 π)/3ã?? )+sin^(-1)â?¡(sinâ?¡ã??(2 π)/3ã?? )

Differentiate tan-1[(√(1+ x^2 ) -1)/x] w.r.t. x

If e^x ã??+eã??^y=e^(x+y), prove that dy/dx + e^(y-x)=0

Differentiate cos^(-1)â?¡ã??((x+ √(1-x^2 ))/√2)ã?? w.r.t. x

If y √(x^2+1)=logâ?¡ã??(√(x^2+1)-x)ã??, then show that (x2 +1 ) dy/dx + xy + 1 = 0

Let y = (log x)x + xx cosx, then find dy/dx

(APPLICATION BASED)

If tan-1a + tan-1b + tan-1c = π/2 ; prove that ab + bc +ca = 1

Prove that 2 tan-1(1/2) + tan-1 (1/7) = sin-1(31/(25√2))

Solve cos-1((x^2-1)/(x^2+1)) + tan-1(2x/(x^2-1)) = 2π/3

If x^p y^q=ã??(x+y)ã??^(p+q), prove that dy/dx=y/x

Find dy/dx, if y = sin^(-1) (2θ/(1+ θ^2 )) and x = tan^(-1) (2θ/(1- θ^2 ))

If y = x sin y, prove that xdy/dx =y/(1-x cos y)

Prove that: 2 tan-1(√((a-b)/(a+b)) tanâ?¡ã??x/2ã??) = ã??cosã??^(-1) ((a cosâ?¡x+b)/(a+b cosâ?¡x ))

Discuss the continuity and differentiability of the function f(x) = |x| + |x+1| in the interval (-1,2)

(HOTS)

Prove that tan (π/4+1/2 cos^(-1) a/b) + tan (π/4-1/2 cos^(-1) a/b) = 2b/a

Solve : sin-16x + sin-16√3 x = - π/2

Differentiate sin^(-1)â?¡ã??((3 x+4 √(1-x^2 ))/5)ã?? w.r.t. x

If x = a (cos θ + log tanθ/2) and y = a sin θ, then find the value of (d^2 y)/dx^2 at θ = π/4

If x = tan(1/a logâ?¡y), then show that(1+x^2 ) (d^2 y)/dx^2 +(2x-a)dy/dx=0

If cos-1x + cos-1y + cos-1z = π, then prove that x2 + y2 + z2 + 2xyz = 1

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Comments Lesson Posted on 07 Jun CBSE/Class 12 CBSE/Class 12/Science/Mathematics

Monica Nadar

I am an experienced, qualified teacher and tutor having more than 2 years of experience in teaching Mathematics,...

A limit is a guess of the value of a function or sequence based on the points around it. Limits best explained with a real life scenario example

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Asked on 20 May CBSE/Class 12/Science/Mathematics

Why we Differentiate between different functions?

Answer

Lesson Posted on 14 May CBSE/Class 12/Science/Mathematics Exam Coaching/UPSC Exams Coaching/NDA (National Defence Acadamy and Naval Acadamy) Exam Coaching Tuition/Class VI-VIII Tuition/English

Preparing for Maths Exam for SAT, GRE, NDA-NA & VII to XII Standard of Any Board

Arun Vinayak Joshi

After completing my BE, I gathered 33 years of industry experience by working in a variety of small-scale...

First, prepare a Formulae Notebook to make Ready Reference for solving the problems. Prepare Index page, write chapter numbers and number all pages of Notebook. Write Chapterwise formulae and mention respective chapter-wise page numbers in the Index page. Start solving problems in a separate notebook... read more

First, prepare a Formulae Notebook to make Ready Reference for solving the problems.

Prepare Index page, write chapter numbers and number all pages of Notebook.

Write Chapterwise formulae and mention respective chapter-wise page numbers in the Index page.

Start solving problems in a separate notebook keeping Formulae Notebook handy. Write all the steps and calculations.

If your answers do not match with the answers given, first check your steps and calculations for errors, and correct them. If it does not match, then only refer to the Answers & Explanations or guide-book.

Give priority to Correctness. Once the practise exercises are over, Go ahead for question paper set or test series. Keep away Formulae Notebook and keep alarm clock to alert you about Exam Time of 3 hours or as the case may be. This way you can get the assessment of your speed.

Some necessary Tables of 2 to 30, Squares of 1 to 30, Cubes of 1 to 30, Rules of divisibility by numbers 2,3,4,5,9 & 11 may also be kept handy if forgotten.

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Comments Asked on 02 May CBSE/Class 12/Science/Mathematics

There was a mistake while typing my phone number, and now the changed no is not being accepted stating... read more

There was a mistake while typing my phone number, and now the changed no is not being accepted stating the no is already in use how to change as it is not accepting a fresh application

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Answered on 29/01/2017 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC)

Prashanth K

Technical Trainer

Row and column wise arrangement of data.

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