TS EAMCET · Maths · Continuity and Differentiability
A function \(f: R \rightarrow R\) is such that \(y f(x+y)+\cos m x y=1+y f(x)\). If \(m=2\), then \(f^1(x)=\)
- A \(-2 \sin 2 x y\)
- B \(4 x\)
- C \(\frac{2 \sin 2 x y}{y}\)
- D \(2 x^2\)
Answer & Solution
Correct Answer
(D) \(2 x^2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text y(f(x+y)-f(x))=1-\cos m x y \\ & \Rightarrow f(x+y)-f(x)=\frac{1-\cos 2 x y}{y} \\ & \Rightarrow \frac{f(x+y)-f(x)}{y}=\frac{2 \sin ^2 x y}{y^2} \end{aligned}\) Let \(y \rightarrow 0\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the roots of the equation exceed , thenTS EAMCET 2018 Easy
- If the minimum value of the quadratic expression \(x^2+5 x-2\) is \(M\) and it exists at \(a\), then \(\frac{M}{a}\) is equal toTS EAMCET 2021 Easy
- TS EAMCET 2022 Easy
- If the point \(z=(1+i)(1+2 i)(1+3 i) \ldots\) \((1+10 i)\) lies on a circle with centre at origin and radius \(r\), then \(r^2\) is equal toTS EAMCET 2016 Easy
- If \(f(x)\) is a real valued function defined by \(f(x)=\frac{a x^{10}+b x^8+c x^6+d x^4+e x^2+12 x+15}{x}\) \((x \neq 0)\) and \(f(4)=-4\), then \(f(-4)=\)TS EAMCET 2023 Easy
- If two circles \(x^2+y^2-6 x-6 y+13=0\) and \(x^2+y^2-8 y\) \(+9=0\) intersect at \(\mathrm{A}\) and \(\mathrm{B}\), then the focus of the parabola whose directrix is the line \(A B\) and vertex is the point \(O\) \((0,0)\) isTS EAMCET 2023 Medium
More PYQs from TS EAMCET
- A ball moving with a velocity \(v\), collides head on with a stationary second ball of same mass. After the collision, the velocity of the first ball is reduced to \(0.15 v\). The kinetic energy of the system is decreased nearly byTS EAMCET 2018 Easy
- The deceleration of a car traveling on a straight highway is a function of its instantaneous velocity \(v\) given by \(\omega=a \sqrt{v}\), where \(a\) is a constant. If the initial velocity of the car is \(60 \mathrm{~km} / \mathrm{h}\), the distance of the car will travel and the time it takes before it stops areTS EAMCET 2017 Medium
- If the electric field of a plane electromagnetic wave is \(\mathrm{E}_z=60 \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} \mathrm{t}\right) \mathrm{Vm}^{-1}\), then the magnetic field of the wave isTS EAMCET 2025 Medium
- If the family of curves \(y=a e^{4 x}+b e^{-x}\), where \(a, b\) are arbitrary constants represents the general solution of the differential equation \(f\left(x, y \frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)=0\), then \(\frac{d f}{d x}=\)TS EAMCET 2020 Medium
- The displacement 's' of a body of mass \(3 \mathrm{~kg}\) under the action of a force is given by \(s=\frac{t^3}{3}\), where ' \(s\) ' is in metres and ' \(t\) ' is in seconds. The work done by the force in the first two seconds isTS EAMCET 2023 Medium
- The area (in sq. units) of the triangle formed by the lines \(x^2-3 x y+y^2=0\) and \(x+y+1=0\), isTS EAMCET 2014 Medium