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11TH · MATH

Question 3

menu_bookSolutionmenu_bookTheorymenu_book•(i)1−x1+x≈1−32x\dfrac{1-x}{\sqrt{1+x}} \approx 1 - \dfrac{3}{2}x1+x​1−x​≈1−23​xmenu_book•(ii)1+2x1−x≈1+32x\dfrac{\sqrt{1+2x}}{\sqrt{1-x}} \approx 1 + \dfrac{3}{2}x1−x​1+2x​​≈1+23​xmenu_book•(iii)(9+7x)1/2−(16+3x)1/44+5x≈14−17384x\dfrac{(9+7x)^{1/2} - (16+3x)^{1/4}}{4+5x} \approx \dfrac{1}{4} - \dfrac{17}{384}x4+5x(9+7x)1/2−(16+3x)1/4​≈41​−38417​xmenu_book•(iv)4+x(1−x)3≈2+254x\dfrac{\sqrt{4+x}}{(1-x)^3} \approx 2 + \dfrac{25}{4}x(1−x)34+x​​≈2+425​x
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11TH · MATH

Question 3

menu_bookSolutionmenu_bookTheorymenu_book•(i)1−x1+x≈1−32x\dfrac{1-x}{\sqrt{1+x}} \approx 1 - \dfrac{3}{2}x1+x​1−x​≈1−23​xmenu_book•(ii)1+2x1−x≈1+32x\dfrac{\sqrt{1+2x}}{\sqrt{1-x}} \approx 1 + \dfrac{3}{2}x1−x​1+2x​​≈1+23​xmenu_book•(iii)(9+7x)1/2−(16+3x)1/44+5x≈14−17384x\dfrac{(9+7x)^{1/2} - (16+3x)^{1/4}}{4+5x} \approx \dfrac{1}{4} - \dfrac{17}{384}x4+5x(9+7x)1/2−(16+3x)1/4​≈41​−38417​xmenu_book•(iv)4+x(1−x)3≈2+254x\dfrac{\sqrt{4+x}}{(1-x)^3} \approx 2 + \dfrac{25}{4}x(1−x)34+x​​≈2+425​x
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Accedmychevron_right11thchevron_rightmathchevron_rightMathematical Inductions And Binomial Theoremchevron_rightExercise 8.3
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