iit jee exam pattern JEE Limits, Continuity and Differentiability | Calculus | Target JEE | Solved Questions | JEE Maths

JEE Advanced Level solved questions and Chapter analysis of JEE Limits, Continuity and Differentiability with Karthik Sir.
We enter the world of Calculus for the first time starting with Limits, Continuity and Differentiability. Starting with limits, we look into the definition and existence of limits, understand the various algebra involving limits. We then have a look at the various indeterminate forms of limits and see the various theorems present to tackle those indeterminate forms. We then move on to understand continuity and differentiability. Look at the types of discontinuities and the connection between continuity and differentiability of a curve.

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Question 1: We look into a limit question involving Greatest Integer Function. The basics of limits is used to tackle this where the left hand limit and right hand limit are individually found out and then first check if limit exists and then the limit is found. 08:35

Question 2: We look into a limit problem involving limit tending to infinity. Even though the problem being an indeterminate form, L’Hospital’s rule is avoided and anything upon infinity tends to zero logic is used to evaluate quickly, a standard trick for evaluating limit tending to infinity problem. 13:18

Question 3: We look at the all time favourite L’Hospital’s Rule to proceed with the given indeterminate form and understand that if limit is existing for something having denominator zero then the limit has to be an indeterminate form. 18:01

Question 4: We look into a limit problem involving limit tending to infinity. The standard trick for limit tending to infinity of anything upon infinity tends to zero logic fails here as the variable is in exponents. Hence we look into the logic of anything between 0 and 1 and raised to infinity tends to zero logic here. 23:01

Question 5: A classic problem of combination of concepts from Algebra and Calculus. Even though it is a rather standard indeterminate form involving limit tending to zero of sin x upon x, the crux of the problem lies in understanding the roots of a quadratic equation. 25:50

Question 6: A continuity and differentiability problem which depends mostly upon understanding of quadratic functions, linear functions, exponential functions and modulus functions and graphing of them. A graphical problem, very less on actual algebraic calculations. 32:11

Question 7: A problem targeting the understanding the correlation between continuity and differentiability of a function at a point. A differentiable function is always continuous at all its points in its domain. 40:36

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#Limits #Continuity #Differentiability #Calculus #IITJEE #JEE #JEEPreparation #TargetJEE #JEEAdvanced #JEEMain

iit jee exam pattern JEE Limits, Continuity and Differentiability | Calculus | Target JEE | Solved Questions | JEE Maths
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