Fill in the boxes- -2-3-1-6

Let the fraction be xConsider x 2/3=1/60ex0exx=1/6+2/30ex0exx=1× 3/6× 3+2× 6/3× 60ex0exx=3/18+12/180ex0exx=3+12/180ex0exx=15/180ex0exx=5/6Hence, the required fr ...

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Standard XII

Mathematics

Chain Rule of Differentiation

Fill in the b...

Question

Fill in the boxes.
$□ - \frac{2}{3} = \frac{1}{6}$

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Solution

Let the fraction be $x$
Consider
$x - \frac{2}{3} = \frac{1}{6} x = \frac{1}{6} + \frac{2}{3} x = \frac{1 \times 3}{6 \times 3} + \frac{2 \times 6}{3 \times 6} x = \frac{3}{18} + \frac{12}{18} x = \frac{3 + 12}{18} x = \frac{15}{18} x = \frac{5}{6}$
Hence, the required fraction is $\frac{5}{6}$

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$5 \frac{3}{4} - □ = 3 \frac{5}{12}$

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$\frac{3}{10} = \frac{12}{□} = \frac{□}{50} = \frac{□}{60}$

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$□ + \frac{3}{4} = 2 \frac{22}{24}$

If $f = \frac{x}{1 + x^{2}} + \frac{1}{3} {(\frac{x}{1 + x^{2}})}^{3} + \frac{1}{5} {(\frac{x}{1 + x^{2}})}^{5} + . . .$ to $\infty$ and $g = x - \frac{2}{3} x^{3} + \frac{1}{5} x^{5} + \frac{1}{7} x^{7} - \frac{2}{9} x^{9} + . . .$ , then $f = d \times g$ . Find 4d.

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Fill in the boxes.□-23=16

Let the fraction be xConsider x-23=16x=16+23x=1×36×3+2×63×6x=318+1218x=3+1218x=1518x=56Hence, the required fraction is 56

Fill in the boxes.
$□ - \frac{2}{3} = \frac{1}{6}$

Let the fraction be $x$
Consider
$x - \frac{2}{3} = \frac{1}{6} x = \frac{1}{6} + \frac{2}{3} x = \frac{1 \times 3}{6 \times 3} + \frac{2 \times 6}{3 \times 6} x = \frac{3}{18} + \frac{12}{18} x = \frac{3 + 12}{18} x = \frac{15}{18} x = \frac{5}{6}$
Hence, the required fraction is $\frac{5}{6}$