NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q12
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 12
Find dy/dx for y=12(1−cos t), x=10(t−sin t), −π/2<t<π/2.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: 6sin t/[5(1−cos t)] for t≠0; no finite derivative at t=0.
- The parameter derivatives are yₜ=12sin t and xₜ=10(1−cos t).
- For t≠0, divide: dy/dx=6sin t/[5(1−cos t)].
- At 0, the quotient is not defined. Expansions x∼(5/3)t³, y∼6t² give a vertical cusp; the slope diverges with opposite signs.
Master Chapter 5: Continuity And Differentiability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
← Previous Question
Differentiate \(x^{x^{2} - 3} + \left(x - 3\right)^{x^{2}}\) with…
Next Question →Differentiate y=sin⁻¹x+sin⁻¹√(1−x²), 0<x<1.
All Questions in Continuity And Differentiability — Miscellaneous Exercise
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?