Quèstion 3 1 Given that the series T converges where P> which of the following is true *- 10 5n + O a. The integral J dx converges 10 (x+ 1)- 2n 2x Ob. - 10 ( 5n" + 10 (5x + 1)? O c. No correct answer O d. The integral , converges (x² + 1)7 dx e. The integral J 10 (x+ 1) 1 dx diverges

Q: 2 1 dx 8 dx 1 dx 1 dx 2 X 6 8 X 1 which one is true? (a) {an} diverges to +o (b) {an} diverges to -o…

A:

Q: Which infinite series below converges to the value of | sinx dx? OA. 1+ 19• 2! 1 1 + 37• 4!' 55• 61…

A:

Q: 1 Q5. Fact: the series S = > converges by virtue of the Integral Test. m(ln m)4 m=3 According to the…

A:

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: Find the 3rd degree Maclaurin Polynomial for f(x) = 2". d -b² = In(b) · b². dx Recall that T3(x)…

A: We will use the basic knowledge of derivatives and the McLaurin series to answer all the three parts…

Q: (14) 3+ Cos (8x) dx Determe by

A:

Q: En-o(1 +)" CO 5n ii) 2n-0 100 (Зп)!

A:

Q: •* In (x) dx. 2x2 Evaluate (Express numbers in exact form. Use symbolic notation and fractions where…

A: Given: ∫2∞lnx2x2dx To do: Evaluate the given integral.

Q: Σ Use the Maclaurin series x" to find a Maclaurin series for the function f(x)= 1-x 2+3x n=0

A: Find  Maclaurin series for the function f(x)=52+3x.

Q: Let the improper integrals " sin(-)dx and sin?()dx (i) Write down the first 3 terms of Maclaurin…

A:

Q: 1. Find a power series representation for the function f(x) = 5x2- Determine the interval of…

A:

Q: 1. determine if it diverges or converges n e2n n=1

A:

Q: Find the sum of the convergent series. Στο(-3)"

A: Given the seriesThe series is a geometric series with common ratio r=−56 and the first term a=1.The…

Q: find the series' interval of convergence and, within its interval, the sum of the series as a…

A:

Q: Q5. Let the improper integrals, sin()dx and sin² ()dx (i) (ii) Write down the first 3 terms of…

A: Introduction: Sometimes the Maclaurin series is very efficient to integrate a function. The power…

Q: The overall, closed-loop, controlled dynamics of a space satellite system can be approximated as: 6,…

A: Here, we need to find θo(t) as a function of the time of the following differential equation.…

Q: 100 Two series E, x, and Yn that both diverge but where , xnYn converges.

A:

Q: 1 Given that the series 2 (1n² + 1)’ 7 converges where P > which of the following is true *-5 O a.…

A: Given series ∑n=5∞6nn2+1p converges where p>12 We have to check which of the given option are…

Q: Prove that 2e 5 2 sin (Tx/4)+1/2 dx ≤ 2e-1 1+2√2 (i) Show that zloga 7/4 dx - (log) (log x)-3/4 (ii)…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Q: By recognizing the series ((1/2))² ((1/2))³ 2 3 sum = ((1/2))" n -((1/2)) + + (−1)”. as a Taylor…

A: