dX 2) Show that ? Xe converges/diverges.

Q: Q2 Prove that the scries 2+ x2 3+X2 4+x is Unitormly convergem? in any interval?

A: The given series is: 11+x2+12+x2+13+x2+……. Therefore the given series can be written as:…

Q: 1 (x + 1)2 dx -2

A:

Q: The improper integral 2e dx is: -00 (a)converge to 2 (b) converge to - 2 (c) converge to 0 (d)…

A: In this question we have to define the integral.

Q: The integral Jo x°dx converges when a < 0 True False

A: Given integral is ∫0∞xαdx with α≤0 we check the value of integral for α≤0

Q: 1 dx is convergent True False

A: Definite integration

Q: Determine if +∞o 5 dx √x-1 is convergent or divergent.

A: Solve the improper integral then using expansion at infinity solve limit

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

A:

Q: Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

A:

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: 00 Determine whether the improper integral ²+37+1 e dx converges or diverges. Show all your steps.

A: Since there is infinity in the upper bound, this is improper integral of type 1.   To evaluate an…

Q: Determine whether the doubly infinite improper integral converges and, if so, evalute it dx (2²+6)/2

A: ................(1) substitute  take derivative put all values in equation 1

Q: The improper integral | 2e*dx is: -00 (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d)…

A:

Q: 0o Inx dx Evaluate it and state whether it converges or diverges. x2 d)

A: That's easy. Have a good day!!!

Q: 1 x + ex 2 g dx

A:

Q: Show that if a&gt;-1 and b&gt;a+1 , then the followingintegral is convergent.

A:

Q: 1/x e 7 dx y3 -1

A:

Q: Determine whether or not the infinite series below converges.

A:

Q: 30. Determine if the integral dx is convergent or divergent c. Neither a. Convergent b. Divergent d.…

A:

Q: dx Jx +x²

A: Please see the below picture for detailed solution.

Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: Perform a test to determine if it converge or diverge -1 x 2sin 1 dx 1– x -1

A: The function is given by: ∫-112sin-1x1-xdx If the function fx=2sin-1x1-x is positive, continuous and…

Q: Which test to use and is it convergent/divergent? 1 Σ Z 16n2 – 8n – 3 n=1

A:

Q: 00 6n–1 Зп+2 1 Apply the nth term divergence test to conclude if E converges or diverges.

A: The divergence of a series can be found using the nth term test. Consider the series . Let . If…

Q: Determine whether

A: Solution: Consider the given integral equation: J = ∫-11dxx1/3 Since the given integrand is defined…

Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d) diverge

A: To solve the given improper integral.

Q: 1 dx et+ e

A:

Q: A. converges B. diverges

A: Given that the series: A. ∑n=1∞15n B. ∑n=1∞n+6n2+12n+4 To find check the series converges or…

Q: In(z2) dz Is the improper integral convergent or divergent? Solve for its value.

A: So, we will solve this integral using by-parts formula Integral I = ∫-10ln(z2) dz We can write this…

Q: Use the Comparison Theorem to de x + 1 36 dx Ji O convergent O divergent 8

A:

Q: Find 2x dx. (if it converges)

A: Idea: use substitution method to integrate  then we get undefined value  so integral is not convert

Q: . Determine whether I = dx converges or diverges. If it converges, find its value. %3D r5/2

A:

Q: Determine if H conver or diverges. Evaluate i it ges converges dx 3

A: We have to find convergence and divergence of integral .Integral is shown as below:

Q: Determine whether r{(1+E)*"}.. Converges or diverges.

A:

Q: 4. Which comparison would show that dx converges? x + e*

A: According to the given information, it is required to tell which comparison would show that the…

Q: dx To determine if converges or diverges, it would be useful to compare the integrand directly to 1

A: Given integral ∫2∞dxx2-1   We have to find it's converges or not . We just use comparison test to…

Q: 00 . does Srea dx converge? Jx te3x

A:

Q: 00 Q5. Evaluate , e z dx if it converges.

A:

Q: dX Show that Xe* converges/diverges.

A: Given : an  = 1 / x e(x)^2

Q: 6. S o Inx dx Evaluate it and state whether it converges or diverges. 1 х2

A: Given: I=∫0∞lnxx2dx

Q: Which test to use and is it convergent/divergent? Σ 16n2 – 8n – 3 n=1 - -

A: Use the ratio test, L=limn→∞an+1an=limn→∞116n+12-8n+1-3116n2-8n-3=limn→∞16n2-8n-316n+12-8n+1-3

Q: o Inx 2. For p>1, is S, dx convergent? 1 xP

A: It is the improper integral of first kind , limit of integration is infinity. There is so many test,…

Q: dx and state whether it converges or diverges.

A: Given that a infinite integration and we find it is converges or diverses. We know that Converse…

Q: n=1 3" 2n2 M.

A: We shall use elementary knowledge of Series and summations to answer this question. Note that…

Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

A:

Q: Σ-(, n=1 n7/2 Put 'C' below if the integral converges, or 'D' if it diverges.

A:

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

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Q: The integral 1 dx is convergent x1.10 Select one: True False

A: We have to check

Q: Perform a test to determine if dx converges or diverges. - 0o Vx° +6

A:

Q: -dx converges ex - e- Select one: O True O False

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!