Assertion Reasoning - Worksheet 1

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Chapter 5 Class 12 - Continuity & Differentiability - Assertion and Reasoning Worksheet 1 by teachoo Chapter: Chapter 5 Class 12 - Continuity & Differentiability Name: _____________________________ School: _____________________________ Roll Number: _____________________________ Instructions: For each question, two statements are given: Assertion (A) and Reason (R). Choose the correct option. (a) Both A and R are true, and R is the correct explanation of A. (b) Both A and R are true, but R is not the correct explanation of A. (c) A is true, but R is false. (d) A is false, but R is true. Assertion (A): The function f(x)=|x-3| is continuous at x=3. Reason (R): Every polynomial function is continuous at every point. Assertion (A): A function must be continuous at a point if it is differentiable at that point. Reason (R): If the limit of a function exists at a point, it must be differentiable at that point. Assertion (A): The function f(x)=cos⁡|x| is differentiable at x=0. Reason (R): The cosine function is an even function, so cos⁡(-x)=cos⁡(x). Assertion (A): The function f(x)=log⁡(x) is continuous for all x>0. Reason (R): The graph of log⁡(x) can be drawn without lifting the pen for all x in its domain. Assertion (A): The derivative of f(x)=x^x with respect to x is x⋅x^(x-1). Reason (R): The power rule for differentiation states that d/dx (x^n )=nx^(n-1). Important links Answer of this worksheet - https://www.teachoo.com/25576/5354/Assertion-Reasoning---Worksheet-1/category/Teachoo-Questions---Assertion-Reasoning/ Full Chapter with Explanation, Activity, Worksheets and more – https://www.teachoo.com/subjects/cbse-maths/class-12th/ Maths Class 12 - https://www.teachoo.com/subjects/cbse-maths/class-12th/ For more worksheets, ad-free videos and Sample Papers – subscribe to Teachoo Black here - https://www.teachoo.com/black/   Answer Key to Assertion & Reasoning - Worksheet 1 b) Both A and R are true but R is not the correct explanation of A . ( f(x)=|x-3| is continuous because it's a composition of continuous functions, not because it's a polynomial). c) A is true but R is false. (Differentiability implies continuity. However, the existence of a limit does not imply differentiability, as seen with f(x)=|x| at x=0 ). a) Both A and R are true and R is the correct explanation of A . (Since cos⁡(x) is an even function, cos⁡|x|=cos⁡(x), which is a standard differentiable function). a) Both A and R are true and R is the correct explanation of A. (The reason is the intuitive definition of continuity). d) A is false but R is true. (The derivative of x^x requires logarithmic differentiation. The power rule in R is correct but only applies when the exponent is a constant).