Question: Write out the form of the partial
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.
Transcribed Image Text:
x* + 1 (a) x* + 4x 1 (b) (x² – 9)²
> Find a polar equation for the curve represented by the given Cartesian equation. x + y = 9
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> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. t* + t? + 1 (a) x* - 1 (b) (t2 + 1)(1? + 4)?
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> (a). If is a complex-valued function of a real variable, its indefinite integral f u (x) dx is an antiderivative of u. Evaluate (b). By considering the real and imaginary parts of the integral in part (a), evaluate the real integrals (c). Compare wit
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> Evaluate the integral. f x2 – 2x – 1/ (x – 1)2 (x2 + 1), dx
> Evaluate the integral. f 10/ (x – 1) (x2 + 9), dx
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> Match the polar equations with the graphs labeled I–VI. Give reasons for your choices. (Don’t use a graphing device.) I II III IV V VI (a) r = Ve, 0<0 < 167 (b) r= 0², 0< 0< 167 (c) r= cos(0/3) (e) r = 2 + sin 30
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> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. 2x 1 (a) (x + 3)(3x + 1) (b) x + 2x? + x
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> Write the sum in expanded form. ∑ni=1 i10
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> Write the sum in expanded form. ∑4k=1 2k – 1/ 2k + 1
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> (a). In Example 11 the graphs suggest that the limaçon r = 1 + c sin θ has an inner loop when |c| > 1. Prove that this is true, and find the values of θ that correspond to the inner loop. (b). From Figure 19 it a
> Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed ibn Alhusain Alkarchi in about AD 1010. The figure shows a square ABCD in which sides AB and AD have been divided into segments of lengths ,1, 2, . . . n, Thus the s
> Write the sum in expanded form. ∑6i=4 i3
> Prove formula (e) of Theorem 3 using a method similar to that of Example 5, Solution 1 [start with (1 + i)4 – i4].
> Prove formula (e) of Theorem 3 using mathematical induction.
> Prove formula (b) of Theorem 3.
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> Find the value of the sum. ∑ni=1 (t3 – i - 2)
> Find the value of the sum. ∑ni=1 (i + 1) (i + 2)
> Find the value of the sum. ∑ni=1 (i + 1) (i + 2)
> Find the value of the sum. ∑ni=1 (3 + 2i)2
> If f is a quadratic function such that f (0) = 1 and f f (x)/ x2 (x + 1)3, dx is a rational function, find the value of f'(0).
> Find the value of the sum. ∑ni=1 (i2 + 3i + 4)
> Find the value of the sum. ∑ni=1 (2 – 5i)
> Write the sum in expanded form. ∑6i=4 3i
> Find the value of the sum. ∑ni=1 2i
> Find the value of the sum. ∑4i=-2 23-i
> Find the value of the sum. ∑4i=0 (2i + i2)
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> Find the value of the sum. ∑8k=0 cos kπ
