Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 0 end subscript space 2 over x log space left parenthesis 1 plus x right parenthesis$

2
1
0
l $\log x$

hint Hint:

Using L’Hospital’s rule, solve the sum.

The correct answer is: 2

$L e t y equals limit as x rightwards arrow 0 of 2 over x log open parentheses 1 plus x close parentheses y equals 2 limit as x rightwards arrow 0 of fraction numerator log open parentheses 1 plus x close parentheses over denominator x end fraction U sin g space L apostrophe H o s p i t a l apostrophe s space r u l e. y equals 2 limit as x rightwards arrow 0 of open parentheses fraction numerator fraction numerator 1 over denominator 1 plus x end fraction over denominator 1 end fraction close parentheses y equals 2 limit as x rightwards arrow 0 of fraction numerator 1 over denominator 1 plus x end fraction y equals 2 open parentheses fraction numerator 1 over denominator 1 plus 0 end fraction close parentheses therefore y equals 2$

L’Hospital’s rule is a general method of evaluating indeterminate forms such as 0/0 or ∞/∞. L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or $\infty / \infty$ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

$Lt subscript x not stretchy rightwards arrow 0 end subscript open parentheses 1 plus fraction numerator 2 x over denominator 3 end fraction close parentheses to the power of 1 over x end exponent$

Maths-General

General

Maths-

$stack L t with x not stretchy rightwards arrow negative 1.5 below cos to the power of negative 1 end exponent space open parentheses fraction numerator x plus 3 over denominator 3 end fraction close parentheses$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow 2 end subscript space log subscript 10 space open square brackets x to the power of 6 plus square root of x squared plus 1292 end root close square brackets$

Maths-General

General

Maths-

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space x over denominator x not stretchy rightwards arrow 0 end fraction 1 over x squared$

Maths-General

General

Maths-

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x to the power of 0 minus sin space 3 x to the power of 8 over denominator x cubed end fraction$

Maths-General

General

chemistry-

Gas masks containing activated charcoal to remove poisonous gases from atmosphere acts on the principle of :

chemistry-General

General

biology

Match the items in column I and column II and choose the correct option:

The correct match is:

biologyGeneral

General

physics-

If by mistake Ammeter is connected parallel to the resistance then i-v curve expected is (Here i = reading of ammeter, v=reading of voltmeter)

physics-General

General

physics-

i v/s V curve for a non-ohmic resistance is shown. The dynamic resistance is maximum at point

physics-General

General

physics-

If emf of battery is 100 V, then what was the resistance of Rheostat adjusted at reading ( i=2A,V=20V)

physics-General

General

physics-

In the experiment, the curve between VX andVW is shown as dotted line (A) If we use an another wire of same material, but with double length and double radius. Which of the curve is expected.

physics-General

General

physics-

The adjacent graph shows the extra extension (Vx) of a wire length 1m suspended from the top of a roof at one end with an extra load Vw connected to the other end . If the cross sectional area of the wire is $10 to the power of negative 6 end exponent m to the power of 2 end exponent$ , calculate the Young’s modulus of the material of the wire.

physics-General

General

chemistry-

Catalyst only

chemistry-General

General

maths-

If $text end text f colon left square bracket negative 2 comma 2 right square bracket rightwards arrow R text is end text$ defined by $f left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator square root of 1 plus c x end root minus square root of 1 minus c x end root over denominator x end fraction comma text end text text f end text text o end text text r end text text end text minus 2 less or equal than x less than 0 end cell row cell fraction numerator x plus 3 over denominator x plus 1 end fraction comma text end text text f end text text o end text text r end text text end text 0 less or equal than x less or equal than 2 end cell end table close$ is continuous on [-2,2] then c =

maths-General

General

Maths-

$L subscript t not stretchy rightwards arrow 2 end subscript fraction numerator vertical line x minus 2 vertical line over denominator x minus 2 end fraction$

Maths-General

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2 1 0 l

Using L’Hospital’s rule, solve the sum.

The correct answer is: 2

Related Questions to study

Gas masks containing activated charcoal to remove poisonous gases from atmosphere acts on the principle of :

Gas masks containing activated charcoal to remove poisonous gases from atmosphere acts on the principle of :

Match the items in column I and column II and choose the correct option:The correct match is:

Match the items in column I and column II and choose the correct option:The correct match is:

If by mistake Ammeter is connected parallel to the resistance then i-v curve expected is (Here i = reading of ammeter, v=reading of voltmeter)

If by mistake Ammeter is connected parallel to the resistance then i-v curve expected is (Here i = reading of ammeter, v=reading of voltmeter)

i v/s V curve for a non-ohmic resistance is shown. The dynamic resistance is maximum at point

i v/s V curve for a non-ohmic resistance is shown. The dynamic resistance is maximum at point

If emf of battery is 100 V, then what was the resistance of Rheostat adjusted at reading ( i=2A,V=20V)

If emf of battery is 100 V, then what was the resistance of Rheostat adjusted at reading ( i=2A,V=20V)

In the experiment, the curve between VX andVW is shown as dotted line (A) If we use an another wire of same material, but with double length and double radius. Which of the curve is expected.

In the experiment, the curve between VX andVW is shown as dotted line (A) If we use an another wire of same material, but with double length and double radius. Which of the curve is expected.

The adjacent graph shows the extra extension (Vx) of a wire length 1m suspended from the top of a roof at one end with an extra load Vw connected to the other end . If the cross sectional area of the wire is , calculate the Young’s modulus of the material of the wire.

The adjacent graph shows the extra extension (Vx) of a wire length 1m suspended from the top of a roof at one end with an extra load Vw connected to the other end . If the cross sectional area of the wire is , calculate the Young’s modulus of the material of the wire.

Catalyst only

Catalyst only

If defined by is continuous on [-2,2] then c =

If defined by is continuous on [-2,2] then c =

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2
1
0
l $\log x$

Match the items in column I and column II and choose the correct option:

The correct match is:

Match the items in column I and column II and choose the correct option:

The correct match is: