Question:
The first non-zero term in the Taylor series expansion of \((1-x)-e^{-x}\) about \( x = 0 \) is
The first non-zero term in the Taylor series expansion of \((1-x)-e^{-x}\) about \( x = 0 \) is
Updated On: Jul 17, 2024
- 1
- -1
- \(\frac{x^2}{2}\)
- \(-\frac{x^2}{2}\)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D) :\(-\frac{x^2}{2}\)
Was this answer helpful?
0
0
Top Questions on Taylor series
- In the Taylor series expansion of sin z around \(z = 0\), the coefficient of the term \(z^3\) is
- GATE PI - 2024
- Engineering Mathematics
- Taylor series
- Consider the function f(x) = ln(sin(x)). Expand f(x+h) using Taylor's series. In this context, the correct statement(s) is/are
- GATE ES - 2024
- Mathematics Foundation
- Taylor series
- The first non-zero term in the taylor series expansion of (1 - x) - e- x, about x = 0
- GATE CH
- Engineering Mathematics
- Taylor series
Questions Asked in GATE CH exam
- Water of density 1000 kg/m³ is pumped at a volumetric flow rate of \( 3.14 \times 10^{-2} \) m³/s through a pipe of inner diameter 10 cm and length 100 m, from a large Reservoir 1 to another large Reservoir 2 at a height of 50 m above Reservoir 1, as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy friction factor \( f = 0.06 \) and a kinetic energy correction factor \( \alpha = 1 \). Take \( g = 9.8 \) m/s². If all minor losses are negligible and the pump efficiency is 100%, the pump power, in kW, rounded off to 2 decimal places, is _____.
- GATE CH - 2024
- Macroscopic friction factors
- Methane combusts with air in a furnace according to the reaction \( \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \). The heat of reaction \( \Delta H_{\text{rxn}} \) is -880 kJ per mol of CH4 and is assumed constant. The furnace is well-insulated, and no side reactions occur. All components behave as ideal gases with a constant molar heat capacity of 44 J mol\(^{-1}\) °C\(^{-1}\). Air is composed of 20 mol% O2 and 80 mol% N2. The air-fuel mixture enters the furnace at 50°C. The methane conversion \( X \) varies with the air-to-methane mole ratio \( r \) as \( X = 1 - 0.1 e^{-2(r-r_s)} \) with \( 0.9 r_s \leq r \leq 1.1 r_s \), where \( r_s \) is the stoichiometric air-to-methane mole ratio. For \( r = 1.05 r_s \), the exit flue gas temperature in °C, rounded off to 1 decimal place, is _____.
- GATE CH - 2024
- Heat of reaction
- A solid slab of thickness \( H1 \) is initially at a uniform temperature \( T0 \). At time \( t = 0 \), the temperature of the top surface at \( y = H1 \) is increased to \( T1 \), while the bottom surface at \( y = 0 \) is maintained at \( T0 \) for \( t \geq 0 \). Assume heat transfer occurs only in the \( y \)-direction, and all thermal properties of the slab are constant. The time required for the temperature at \( y = \frac{H1}{2} \) to reach 99% of its final steady value is \( T1 \). If the thickness of the slab is doubled to \( H2 = 2H1 \), and the time required for the temperature at \( y = \frac{H2}{2} \) to reach 99% of its final steady value is \( T2 \), then \( \frac{T2}{T1} \) is .
- GATE CH - 2024
- Heat Transfer
- The temperatures of two large parallel plates of equal emissivity are 900 K and 300 K. A reflection radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in K, is
- GATE CH - 2024
- Heat Transfer
- Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol m\(^{-3}\) and 6 mol m\(^{-3}\), respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is:
- GATE CH - 2024
- Phase equilibria
View More Questions