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# 4th - MATH 120 RECITATION QUESTIONS WEEK 4 1 Find the...

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MATH 120 RECITATION QUESTIONS WEEK 4 1. Find the Maclaurin series for f ( x ) = (1 + x ) - 3 , and the radius and interval of convergence, also. 2. Find the Maclaurin series of f ( x ) = cos x 2 and its radius of convergence. Compare the graph of f and those of its ﬁrst three Taylor polynomials. 3. Use series to approximate the deﬁnite integral Z 1 0 x cos( x 3 ) dx correct to three decimal places. 4. Use series to evaluate the limits a ) lim x 0 sin x - x + 1 6 x 3 x 5 ; [Ans:1/120] b ) lim x 0 sin(sin x ) - x x [cos(sin x ) - 1] ; [Ans:2/3] 5. Use the binomial series to expand the function f ( x ) = x 4 + x 2 as a power series. State the radius of convergence. 6. Try to attempt L’Hospital Rule to evaluate the limit lim x 0 ( e 2 x - 1) ln(1 + x 3 ) (1 - cos 3 x ) 2 and compare the evaluation (of this limit) using series. [Ans:8/81] 7. Expand f ( x ) = x + x 2 (1 - x ) 3 as a power series and use this to ﬁnd the sum of the series X n =1 n 2 2 n . [Ans:6]

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4th - MATH 120 RECITATION QUESTIONS WEEK 4 1 Find the...

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