Class 12 Continuity And Differentiability · Conceptual Answer1 Marksbranch_sensitive_differentiation
Class 12 Maths · Continuity And Differentiability · Conceptual Answer #113
For y=arctan[(1+tan x)/(1−tan x)], find y′ for −π/4<x<π/4.
✅ Step-by-Step Solution
Final Answer: 1
- The tangent addition formula gives y=arctan(tan(π/4+x))=π/4+x on this open interval, so y′=1.
- 1
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The tangent addition formula gives y=arctan(tan(π/4+x))=π/4+x on this open interval, so y′=1.
- [0.5 marks] 1
Master Chapter 5: Continuity And Differentiability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
← Previous Question
For y=[sin(x/2)+cos(x/2)]², find y′ at x=π/6.
Next Question →For y=ln(e^x), find y′.
More Practice Questions in Continuity And Differentiability
Related Questions in Continuity And Differentiability
Class 12 Continuity And Differentiability · Mcq Single Correct
For k<0, define f(x)=(1−cos(kx))/(x sin x) for nonzero x near 0, and f(0)=1/2. Find k for…
Class 12 Continuity And Differentiability · Mcq Single Correct
Near π/2, f(x)=k cos x/(π−2x) for x≠π/2 and f(π/2)=3. Find k for continuity.
Class 12 Continuity And Differentiability · Mcq Single Correct
Find the full set of real inputs excluded from the natural domain of cot x (its poles).
Class 12 Continuity And Differentiability · Mcq Single Correct
How many real inputs are excluded from the original formula f(x)=(x−1)/[x(x²−1)]?
Class 12 Continuity And Differentiability · Mcq Single Correct
For x≠0, f(x)=(e^(3x)−e^(−5x))/x, and f(0)=k. Find k for continuity at 0.
Class 12 Continuity And Differentiability · Mcq Single Correct
Let f(x)=x/|x| for x<0 and f(x)=−1 for x≥0. What is its complete continuity set?