Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 0 end subscript space open parentheses fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses$

1
0
2

does not exist

hint Hint:

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

The correct answer is: 1

$limit as x rightwards arrow 0 of space open parentheses fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses U sin g space L ’ H o s p i t a l ’ s space r u l e comma equals limit as x rightwards arrow 0 of open parentheses fraction numerator begin display style fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction end style over denominator 1 end fraction close parentheses equals open parentheses fraction numerator 1 over denominator square root of 1 minus open parentheses 0 close parentheses squared end root end fraction close parentheses equals 1$

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.

$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 2 x over denominator tan to the power of negative 1 end exponent space x end fraction$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$

Maths-General

General

Maths-

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

Maths-General

General

Maths-

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

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

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1 0 2 does not exist

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

The correct answer is: 1

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.

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1
0
2

does not exist

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: