The value of <math><mrow><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>1</mn></mrow></munder><mfrac><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mi>s</mi><mi>i</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mi>π</mi><mi>x</mi></mrow><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>−</mo><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></math> is equal to

x4−2x3+2x−1= (x−1)2 (x2−1)sinπx=sin (π (1−x)=−sin (sinπ (x−1))limx→1 (x2−1)⋅sin2πx (x2−1) (x−1)2=limx→1sin2 (π (x−1)) (x−1)2=limx→1sin2 (π (x−1)) (π (x−1))2⋅π2= 2

The value of&nbsp;<math><mrow><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>1</mn></mrow></munder><mfrac><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mi>s</mi><mi>i</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mi>π</mi><mi>x</mi></mrow><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>−</mo><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></math>&nbsp;is equal to

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Integration Maths Integrals Maths Class 12th

The value of $\underset{x \to 1}{l i m} \frac{(x^{2} - 1) s i n^{2} (π x)}{x^{4} - 2 x^{3} + 2 x - 1}$ is equal to

Option 1 -

$\frac{π^{2}}{6}$

Option 2 -

$\frac{π^{2}}{3}$

Option 3 -

$\frac{π^{2}}{2}$

Option 4 -

2 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

3 months ago

Correct Option - 4

Detailed Solution:

$x^{4} - 2 x^{3} + 2 x - 1 = {(x - 1)}^{2} (x^{2} - 1)$

$s i n π x = s i n (π (1 - x)$

$= - s i n (s i n π (x - 1))$

$\underset{x \to 1}{l i m} \frac{(x^{2} - 1) \cdot s i n^{2} π x}{(x^{2} - 1) {(x - 1)}^{2}} = \underset{x \to 1}{l i m} \frac{s i n^{2} (π (x - 1))}{{(x - 1)}^{2}}$

$= \underset{x \to 1}{l i m} \frac{s i n^{2} (π (x - 1))}{{(π (x - 1))}^{2}} \cdot π^{2}$

= 2

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The value of $\underset{x \to 1}{l i m} \frac{(x^{2} - 1) s i n^{2} (π x)}{x^{4} - 2 x^{3} + 2 x - 1}$ is equal to

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The value of limx→1(x2−1)sin2(πx)x4−2x3+2x−1 is equal to

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The value of $\underset{x \to 1}{l i m} \frac{(x^{2} - 1) s i n^{2} (π x)}{x^{4} - 2 x^{3} + 2 x - 1}$ is equal to