GATE ME 2014 Set 2 | Calculus Question 15 | Engineering Mathematics

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GATE ME 2014 Set 2

MCQ (Single Correct Answer)

-0.3

$$\mathop {Lt}\limits_{x \to 0} \left( {{{{e^{2x}} - 1} \over {\sin \left( {4x} \right)}}} \right)\,\,$$ is equal to

$$0$$

$$0.5$$

$$1$$

$$2$$

GATE ME 2014 Set 3

MCQ (Single Correct Answer)

-0.3

If a function is continuous at a point,

the limit of the function may not exist at the point

The function must be derivable at the point

the limit of the function at the point tends to infinity

the limit must exist the point and the value of limit should be same as the value of the function at the point.

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

$$\mathop {Lt}\limits_{x \to 0} {{x - \sin x} \over {1 - \cos x}}$$ is

$$0$$

$$1$$

$$3$$

not defined

GATE ME 2013

MCQ (Single Correct Answer)

-0.3

The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} $$ is

$${4 \over 9}\sqrt {{e^3}} + {2 \over 9}$$

$${2 \over 9}\sqrt {{e^3}} - {4 \over 9}$$

$${2 \over 9}\sqrt {{e^3}} + {4 \over 9}$$

$${4 \over 9}\sqrt {{e^3}} - {2 \over 9}$$

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GATE ME Subjects

Engineering Mechanics

Engineering Mechanics Static and Dynamics

Machine Design

Bolted Riveted and Welded Joints Design For Static Loading Design of Brakes and Clutches Design of Spur Gears Design of Bearings Fatigue Strength

Strength of Materials

Springs Pure Bending Stresses In Beams Simple Stress and Strain Complex Stresses Moment of Inertia Deflection of Beams Shear Force and Bending Moment Torsion Thin Cylinders Columns and Struts Strain Energy Method

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Production Engineering

Metrology and Inspection Sheet Metal Forming Processes Welding Process Metal Forming Metal Cutting Advance Machine Tools Machining Casting

Industrial Engineering

Queuing Production Planning and Control Line Balancing Forecasting Linear Programming Assignment Pert and Cpm Inventory Control Transportation Scheduling

Turbo Machinery

Theory of Machines

Vibrations Gears and Gear Trains Flywheel Analysis of Plane Mechanisms

Engineering Mathematics

Linear Algebra Calculus Vector Calculus Probability and Statistics Differential Equations Complex Variable Transform Theory Numerical Methods

Fluid Mechanics

Fluid Properties Fluid Statics Boundary Layer Turbulent Flow Laminar Flow Fluid Dynamics Fluid Kinematics

Thermodynamics

Calculation of Work and Heat Entropy and Irreversibility Properties of Pure Substances Basic Concepts and Zeroth Law First Law of Thermodynamics Rankine Cycle Availability Second Law of Thermodynamics

General Aptitude

Verbal Ability Numerical Ability