1 Given that the series 2 (1n² + 1)’ 7 converges where P > which of the following is true *-5 O a. The integral J, (x + 1)' dx converges 1 Ob. The integral J- s (x+ 1)- dx converges O. The integral J ;dx diverges (x+ 1) ón бх $(1n² + 1)' (1x + 1)? O e. No correct answer

Q: Find the positive values of x for which the series > xnn is convergent. n= Is the function f(x) = >…

A: Consider the series ∑n=1∞xlnn We have to find positive value of x for which the given series is…

Q: the value of the integral dx 4.x(ln(9x))² 2

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: 6) Find at least four nonzero terms in a power series expansion about x = 0: %3D (1 - x²)y" – y' + y…

A: please see the next step for solution

Q: The coefficient of cos (3x) in the Fourie series of f (x) = –kif – T < x < 0, ƒ (x) = kif 0 < x < a,…

A: Consider the given information: f(x)=-k,-π&lt;x&lt;0 k,0&lt;x&lt;π For finding the coefficient of…

Q: 3. a. Use the binomial series (1 +x)" = E()" to first obtain a series for the function Ax) • Recall…

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: 3. f(x) = Expand the 2π-periodic function π, 0 < x < T 2π-x, π < x < 2π in a Fourier series. In…

A: Here the function is given by fx=π,            0&lt;x&lt;π2π-x,      π&lt;x&lt;2π The 2π- periodic…

Q: Show that Show that Show that fexx dx converges for any p = R. In xdx and f′ (x(ln x)(1 + x²)−¹)dx…

A:

Q: ∞0 Š 7/9 Evaluate 5dx X3 11

A: To evaluate the following integral.Note: Since you have posted multiple questions which are not…

Q: Suppose that ∞ n = 0 anxn converges to a function y such that y'' − 2y' + y = 0 where y(0) = 0 and…

A: We need to find formula.