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First, prove that the following series converges. Second, calculate the number of terms n that must be added in order to find the sum to within 0.001 and type your answer into the answer box. ∑ n = 1 ∞ ( − 1 ) n 4 n 2 {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty (-1)^n \frac{4}{n^2}”}(Show all sufficient work in steps, use the technique or method discussed in this course and include the name of test you used.)

Find the arc length of y=x32{“version”:”1.1″,”math”:”y=x32″} on the interval 2,4{“version”:”1.1″,”math”:”2,4″}. (Show all sufficient work in steps and use the technique or method discussed in this course.)

All of the statements about sinus arrhythmia are true except:

Find a power series for the following function. f ( x ) = ln ⁡ ( 5 − x ) {“version”:”1.1″,”math”:”f(x) = \ln(5-x)”}(Show all sufficient work in steps and use the technique or method discussed in this course.)

Unlike the mammalian heart, the reptilian heart has only three chambers, two atria and one ventricle.

The next two questions are the math questions for the exam. Make sure to write down supporting written work these problems.DO NOT SUBMIT OR CLOSE YOUR TEST before answering all the questions.

Evaluate the following integral: ∫ cos ⁡ x sin 3 ⁡ x   d x {“version”:”1.1″,”math”:”\int \sqrt{\cos x} \sin^3 x ~dx”}(Show all sufficient work in steps and use the technique or method discussed in this course.)

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Set up, but do not evaluate, the integral for the arc length of the parametric curve defined by x ( t ) = 1 3 t 3 y ( t ) = 1 2 t 2 t ∈ [ 0 , 4 ] {“version”:”1.1″,”math”:”\begin{align*} x(t) &= \frac{1}{3} t^3 \\[5pt] y(t) &= \frac{1}{2} t^2 \\[10pt] t &\in [0,4] \end{align*}”}(Show all sufficient work in steps and use the technique or method discussed in this course.)

Evaluate the following integral: ∫ 1 e 3 1 x ln ⁡ x   d x {“version”:”1.1″,”math”:”\int\limits_1^{e^3} \frac{1}{x\sqrt{\ln x}} ~dx”}