(a) (i) Use the linear approximation formula or y ~ f'() f(x+x) f(x) +...
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(a) (i) Use the linear approximation formula or Δy ~ f'(π) Δε f(x+x) ≈ f(x) + f'(x) Ax with f(x)= e to show that etan² (1) sec²(x) for small values of z. (ii) Use the result obtained in part (a) above to approximate */12 */¹² etan²(2) da. (iii) Approximate 1/¹2 etan² (2) dx using Simpson's rule with n = 4 strips. How does the approximate answer in (iii) compare with the approximate answer in (ii)? (b) The period of a pendulum of length L is given by T = 2√√ where g is acceler- 2₁ ation due to gravity. (i) Use the linear approximation formula given above (in part a(i)) to show that if the length of the pendulum increases by AL then the increase in the period is T AT≈ 2L (ii) Give the percentage change in the period, if the length of the pendulum increases by 4%. -AL. (a) (i) Use the linear approximation formula or Δy ~ f'(π) Δε f(x+x) ≈ f(x) + f'(x) Ax with f(x)= e to show that etan² (1) sec²(x) for small values of z. (ii) Use the result obtained in part (a) above to approximate */12 */¹² etan²(2) da. (iii) Approximate 1/¹2 etan² (2) dx using Simpson's rule with n = 4 strips. How does the approximate answer in (iii) compare with the approximate answer in (ii)? (b) The period of a pendulum of length L is given by T = 2√√ where g is acceler- 2₁ ation due to gravity. (i) Use the linear approximation formula given above (in part a(i)) to show that if the length of the pendulum increases by AL then the increase in the period is T AT≈ 2L (ii) Give the percentage change in the period, if the length of the pendulum increases by 4%. -AL.
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a i To show that etan2x sec2x for small values of x using the linear approximation formula well find the derivative of fx ex and evaluate it at x fx e... View the full answer
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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