InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
What will be the nature of the equation (sinθ)/θ for 0 < θ < π/2 if θ increases continuously?(a) Decreases(b) Increases(c) Cannot be determined for 0 < θ < π/2(d) A constant functionThe question was posed to me in an interview for job.This interesting question is from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12 |
|
Answer» CORRECT CHOICE is (a) Decreases To elaborate: Let, f(θ) = (sinθ)/θ Differentiating both sides of (1) with respect to θ we get, f’(x) = (θcosθ – sinθ)/θ^2……….(1) Further, assume that F(θ) = θcosθ – sinθ Then, F’(x) = -θsinθ – cosθ + cosθ = -θsinθ Clearly, F’(x) < 0, when 0 < θ < π/2 Thus, F(θ) < F(0), when 0 < θ < π/2 But F(0) = 0*cos0 – sin0 = 0 Thus, F(θ) < 0, when 0 < θ < π/2 Therefore, from (1) it FOLLOWS that, f’(θ) < 0 in 0 < θ < π/2 Hence, f(θ) = (sinθ)/θ is a decreasing function for 0 < θ < π/2 i.e., for 0 < θ < π/2, f(θ) = (sinθ)/θ steadily decreases as θ continuously increases. |
|