GATE ME 2014 Set 3 | Calculus Question 18 | Engineering Mathematics

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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

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

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

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

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

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is

continuous and differentiable .

non-continuous and differentiable.

continuous and non-differentiable.

neither continuous nor differentiable.

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GATE ME Subjects

Engineering Mechanics

Engineering Mechanics Static and Dynamics

Strength of Materials

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

Theory of Machines

Analysis of Plane Mechanisms Gears and Gear Trains Vibrations Flywheel

Engineering Mathematics

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

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

Fluid Mechanics

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

Turbo Machinery

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Thermodynamics

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

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability