## GATE Data Science and AI Calculus and Optimization Syllabus

**Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.**

Here’s an overview of GATE Data Science and AI Calculus and Optimization Syllabus

**Function**: A function is a relation between a set of inputs (domain) and a set of possible outputs (codomain), where each input is related to exactly one output. It’s often denoted by ( f(x) ), where ( x ) is the input variable.**Limit**: The limit of a function represents the behavior of the function as the input approaches a certain value. It’s denoted as ( \lim_{x \to a} f(x) ) and represents the value that ( f(x) ) approaches as ( x ) approaches ( a ).**Continuity and Differentiability**:- Continuity refers to the property of a function where there are no abrupt jumps or breaks in the graph. A function is continuous at a point ( a ) if the limit of the function exists at ( a ) and is equal to the value of the function at ( a ).
- Differentiability refers to the property of a function where it has a well-defined derivative at each point in its domain.

**Taylor Series**: A Taylor series is an infinite series representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. It’s useful for approximating functions, especially around a specific point.**Maxima and Minima**: Maxima and minima are points where a function reaches its highest or lowest value, respectively. They can occur at critical points where the derivative is zero or undefined, and at endpoints of intervals.**Optimization Involving a Single Variable**: Optimization involves finding the maximum or minimum value of a function within a given domain. This can be achieved by identifying critical points, checking endpoints, and using the first or second derivative test to determine whether a critical point corresponds to a maximum, minimum, or neither.

Understanding these concepts is crucial for analyzing and manipulating functions of a single variable, which are foundational in calculus and mathematical modeling across various disciplines.

GATE DATA SCIENCE AND AI CALCULUS AND OPTIMIZATION FULL COURSE–Just at Rs.300

**GATE DA Subject wise syllabus:**

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