GATE Questions & Answers of Differentiability

What is the Weightage of Differentiability in GATE Exam?

Total 2 Questions have been asked from Differentiability topic of Calculus subject in previous GATE papers. Average marks 1.50.

If $f\left(x\right)=R\;\sin\;\left(\frac{\pi x}2\right)+S,\;f'\left(\frac12\right)=\sqrt2\;and\;\int_0^1f\left(x\right)dx=\frac{2R}\pi, $ then the constants R and S are respectively

The function f(x)=x sin x Satisfies the following equation:f "(x)+f(x)+t cos x=0.the value of t is_________.