Question

if u=3v^7 - 6v, find the percentage error in u at v=1, if the error in v is 0.05​

Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{u = 3 {v}^{7} - 6v}$

TO DETERMINE

The percentage error in u at v = 1 , if the error in v is 0.05

EVALUATION

Here it is given that

$\displaystyle\sf{u = 3 {v}^{7} - 6v}$

Now we have

$\displaystyle\sf{ \Delta u = \frac{du}{dv} \: \Delta v}$

$\displaystyle\sf{ \implies \: \Delta u = (21 {v}^{6} - 6) \: \Delta v}$

$\displaystyle\sf{ \implies \: \Delta u = (21 {v}^{6} - 6) \: \times 0.05}$

Thus at v = 1 the absolute error in computation of u is given by

$\displaystyle\sf{ \implies \: \Delta u = (21 \times {1}^{6} - 6) \: \times 0.05}$

$\displaystyle\sf{ \implies \: \Delta u = (21 - 6) \: \times 0.05}$

$\displaystyle\sf{ \implies \: \Delta u = 15 \: \times 0.05}$

$\displaystyle\sf{ \implies \: \Delta u = 0.75}$

Thus percentage error in u

$\displaystyle\sf{ = \bigg| \frac{\Delta u}{ u} \bigg| \times 100\%}$

$\displaystyle\sf{ = \frac{0.75}{1} \times 100\%}$

$\displaystyle\sf{ = 75 \: \%}$

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