Let An= [n, n+1] and Bn= Lo,3++ for all neN 9 (UAn)= lim ML (An) %3D n-> DO %3D HL ") ML (U Bn ) = 3 NEIN*

Q: O (CA)' = (cl*]) - [ca - [ca - cl27] - C(A') O (CA)T = (cle])" = [ca]' - [] = c[ed] = cta™) O (c4)T…

A:

Q: Integral of 3x^5 + cos^2(5x) + 2sin(x)

A: we need to find the integration of the function

Q: How many four-digit numbers have "9 before g"?

A: Suppose x4x3x2x1 be a four digit number. Therefore x4≠0. To find number of four digit numbers which…

Q: Homework: Find the following 1. L1 (s+ a)2)

A: As per our guidelines we are supposed to answer only one question

Q: 5) Sdve é^ + 3e*- 10 = 0

A: You can solve this question by the substitution method. let ex as some other variable say y. solve…

Q: Compute −∞∫+∞​ x^n e^(−x)^2 dx  for all n∈N

A: Assuming the improper integral is convergent.

Q: Use the method of Substitution to integrate the following 5s * e^(s^2+4)

A:

Q: Find the integral of ∫tan^5(4x)dx

A: Given Data: Integrand: ∫tan54xdx   let u=4x   The derivative of the above equation is, dudx=41dx=du4

Q: Find the inverse Lapace Transform    L^(-1) {1/[(s^2 +9)^2]}

A:

Q: Evaluate the inverse Laplace transform L^-1 { (1 + e^-2s)^2 / (s + 2) }

A: Solution

Q: L, x*e*** dx 3+1

A: 3.1) ∫-12x2e(x3+1)dx Let u=x3+1 du=3x2dx

Q: Let f(x)=x^3 + 5. Explain why f(x) is invertible, then how all steps in the derivation of a formula…

A:

Q: xp (x) + xA + x^) xp (1/) + xA + x^)/ (a) (f) (4 x 87 + 4" + 6" In 6) dr 1 dx x In x (g)

A: Take derivative of each term , apply power rule

Q: power expansion of (e^x)/1-x

A: Given f(x) = ex1 - x

Q: A population of N=6 has a EX^2 =54. What is the value of SS for this population

A: Ans:- Given, A population of N=6 has a EX^2 =54. What is the value of SS for this population

Q: f(x) = e^-1/x^2 show that there is no positive number M such that each natural no n, |f^n(x)|<…

A: We need to prove that there is no positive number M such that each natural number n,

Q: find a closed form expression for ∑(n=0 to ∞) [(n^2)/(2^n)]

A: The expression ∑n=0∞n22n We need to find the closed form of the expression

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

A:

Q: =P(B) =P(A/B) = fnd P (B/A) and P (B/A^) P(A/B) = find P (B/A) and P (B/Aº) %3D

A:

Q: express     n-1 Σ((k^2)/n) k=1   in closed form.

A: The given question is related with closed form of finite sum. Given that,…

Q: Use Heaviside Expansion Theorem (2s^2+1)/[(s-2)(s^2-2s+5)^2]

A:

Q: how does -1 transform into e^((2k+1)TTi)?

A: (.)  Euler's formula is,             we have to show that .

Q: Give a clear and detailed solution of the intergral of e^-ct/m 2)

A: You want intergral of e^-ct/m. I am assumig the variable of integration is "t". That is, the task in…

Q: Find the roots of x^2 + (k^2+1/k) x + 1 = 0

A:

Q: Sketch and graph f(x)=7-2x^2       g(x)=x^2+4 on [-2,6] Shade between them on [-2,6] and write the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 6.89 x10 (0.0136x10) exp[1271.6/{(1.8x60)+127}]=20.98(10-)

A:

Q: fle) sinzdz Compute

A:

Q: find the power serie representation of( (x-2)^6)/e^x n=0 to infinity

A:

Q: How do you derive the reduction formula for integrating sec^3xtan^2x?

A: I am attaching image so that you understand each and every step.

Q: Use the partial fraction decomposition find L^-1[24e^(-5s)/(s^2-9)]

A: We have to find the given laplace inverse transform.

Q: Vs = ft - f- f+ + f =

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.