Once upon a time, in a small town, there was a bright boy named Rahul. He was studying in Class 11. Rahul loved Mathematics and was intrigued by Limits and Derivatives.
One sunny afternoon, Rahul approached his Math teacher, Mr. Smith and asked him if he could help him understand Limits and Derivatives better. Mr. Smith was delighted to see Rahul''s enthusiasm. He started explaining limits.
He started explaining limits using graphs and he showed him how the limit is the value a function approaches as the variable approaches a point. It's like if you're on a trip a 100 miles away, what will be the distance as you get closer and closer to your destination. Mr Smith moved on to Derivatives next and showed Rahul how the derivative is the rate of change of a function at a particular point.
If you're on a road trip, the derivative represents the car's speed at any instant. Rahul realised that he could use the derivative of the distance function to find the speed. As days turned into weeks, Rahul's understanding of limits and derivatives deepened.
He could solve complex problems in limits and he even started helping his classmates with limits and derivatives. With the right approach and determination, even the most challenging mathematical concepts can be learnt.
Limits and Derivatives form the basic foundation of Calculus. It's introduced in Class 11 briefly and followed up extensively in Class 12. Being a math educator teaching mathematics to high school and college students for over 3 decades, I can tell you what exactly you need to be learning in Limits and Derivatives for Class 11. All my students have found Limits and Derivatives incredibly easy after learning from me.
So, here are the best study tips for learning Calculus,- Class 11 Mathematics. When you understand these tips outlined here, you'll be able to solve any question on Limits and Derivatives with ease.
Understanding limits in Class 11 Mathematics
As you come across the definition of a limit for the first time, it says that as x approaches a neighbourhood of a, the function approaches a neighbourhood of l. This may seem a little difficult to comprehend for the first time.
But as I tell my students, when it comes to problem solving, it's as simple as just substituting the value of x, provided the denominator is not zero.
What happens if the denominator is zero? then we work around the function so that the denominator does not tend to zero. Again there are exceptions, but this is the basic rule to follow.
Tip #2 - Learn results on the basic algebra of limits and some important theorems on limits
There are some basic results such as limit of a sum is equal to the sum of limits, limit of a difference is equal to the difference of limits, limit of a product /quotient is equal to the product/quotient of limits. My students find this incredibly easy.
There are also some basic theorems on algebraic limits. What's most important is that you understand the concept of left hand and right hand limits and how to use it in problem solving.
"Knowing limits is essential to understanding Calculus."
Tip #3 - Progress to Trigonometric Limits
Next you will learn about trigonometric limits. There are a couple of formulas used here. The formula of cos2x is used extensively here. As I tell my students, this formula is used practically in every Calculus class. While problem solving, you end up using all the trigonometric formulas that you have learnt.
Tip #4 - Limits of exponential and logarithmic functions and introduction to Derivatives
There are limits of exponential and algebraic functions which are very important as they are used in Class 12 in Indeterminate form of Limits. I have had students using these formulas in college mathematics as well
From here, you will be introduced to derivatives. The very basic definition of a derivative starts with limits. That's precisely why you learn limits first and then derivatives. My students are not particularly fond of evaluating derivatives using the definition. They feel it's much more easier to use the formula and evaluate the derivatives.
But then, as I keep telling them, learning how to use the definition for calculating the derivative is necessary. Moving on, you will come to the formula for calculating derivatives. You need to know certain basic formulas such as algebraic formulas, derivative of a constant and most important derivatives of trigonometric functions.
There is also the product rule and the Quotient rule. My students are able to manage the product rule easily but when it comes to the quotient rule, they get confused initially. But then, with practice they are able to overcome it.
You are also just introduced to the chain rule in Class 11, but then that is just a tip of the iceberg and you'll use it later in Class 12.
Tip #5 - How to get a high score in Calculus Class 11
Just reading this will go a long way in helping you understand Limits and Derivatives in Calculus. I have provided some useful formulas which will go a long way in your study. My students just love it when I give them the formulas readymade. I hope you like it too! To learn more, visit
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Quite a few of them have chosen to pursue Math as their further study. I tutor online and in groups of 5 to 10. You can avail the most convenient option for you. When you join my classes, you'll see your marks rising steadily!
But wait----. The most important takeaway is that you need to practice math on a daily basis to excel in it.. Once you excel in Math, the sky is your limit!
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