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: is intea rable Primitive aR 2 > X 3 1 2. 1 ラメラ 。 (今さ うx 31 ラ× %3D >入う。

A: we have Fx=0            0≤x<12x-1    1≤x≤2and fx=1     0≤x≤12    1≤x≤2 i The primitive of a…

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

A:

Q: /tangent slupe rosin (20) when 5 2) 553 る 653 O not of thc above

A:

Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: Compute the indicated left or right sum for the given functioi ntèrval. 1 L4 for f(x) = on [2,4] %3D

A: We are asked to find the right sum of the integral.

Q: Use (3) from Section 5.4 to evaluate the integral. "In 4 ex dx =

A: INTEGRATION problem.....

Q: السؤال 2 when hv hvo Electron is ejected from surface of metal ylgn O

A: Since we know that​ The ejected electrons have a distribution from 0 to  hv-hv0

Q: Evaluate the integral. 4 (5 - t)Vt dt

A: The objective of the question is evaluate the definite integral.

Q: Fimd dy using Implict die Differentiaten 3xニ3 2. 土

A: Given equation is x2y+3xy3-x=3. To find dydx using implicit differentiation. Solution: Implicit…

Q: Compute 3 In(x² + 1)dx=

A:

Q: Evaluate the integral: */64 – a°dz .3 2 -

A:

Q: 2 sin Sx lim 3x

A: Consider the limit  limx→02sin5x3x

Q: Show by example that Σ(an/bn) may diverge even though Σan and Σbn converge and no bn equals 0.

A:

Q: ) How alutiino a. many ths to the eguotin X, + X2 + X3 +X4 + X5 = 10, uhere poitine integoro ? X,,…

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Q: cos NII 2) Show that converges/diverges.

A:

Q: 6. Let (x,) be properly divergent and let (y,) be such that lim(x,y,) belongs to R. Show that (y,)…

A: To show that (yn) converges to 0, given (xn) is properly divergent and (yn) is such that lim(xnyn)…

Q: 5. Integral ReR dR

A:

Q: What substitutions are sometimes used to transform integrals involving √(a2 - x2), √(a2 + x2), and…

A: The drivers of the substitution to be used in this integral are the trigonometric identities: sin2u…

Q: Find daivative using Ab intiative Methed Of the function 3. |

A: Let the given function be y -y = 3x3+5x2-2x-12Differentiating with respect to x -dydx =…

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: nsist only of of even length. Generalize to find the EGF number of ations that consist only of…

A: To find: (1) The EGF for the number of permutations that consist only of cycles of even length.…

Q: Inn NTT <os 2. n=1

A:

Q: 1う× ) did Fis erimitive af F af F 2) did p is integrable

A:

Q: Which of the following formulas describes an autoregressive (AR) process?

A: Write the AR process (autoregressive process) of order p

Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

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Q: Use linear approximation to approximate the value of In(0.83) two decimal places. In(0.83) ,

A:

Q: Use (3) from Section 5.4 to evaluate the integral. In 2 ex dx = /1

A:

Q: The interval [0, 4] is partitioned into n equal subintervals, and a number x, is arbitrarily chosen…

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Q: How many ways are there to distribute r+s identical balls among five different children such that…

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Q: 8. Show that the sequence f,(2) =. converges uniformaly in the region 1+ na l2l2 2, but does not…

A: Show that the sequence fnz=11+nz converge suniformly in the regionz≥2, but does not converges…

Q: How is l'hopital's rule used for 1^infinity?

A:

Q: 23-4214X Evaluate th integral.

A: The integral is evaluated below

Q: Suppose an 20 and limnan = L.Then 1. If 0 ≤ L < 1, then Enz1an converges

A:

Q: 4. Use the integral expression you wrote in #3 and the Fundamental Theorem of Calculus to find the…

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Q: Establish the 1dentity COSLIT-e)=- čos O Write down the Sequence of Steps that verify iolentity the

A: Given- cosπ-θ=cosθ To Find- The sequence of the steps that verify the above identity. Identity Used-…

Q: 1 Integrate 1+25cosx

A: To evaluate: ∫11+25cosxdx Let, I=∫11+25cosxdx Since, we know that cosx= 1-tan2x21+tan2x2…

Q: 8. S(1- sec3x)²dx

A:

Q: Seuchudu = In) tanh 5 ul +c In tanh %3D

A:

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: Evaluate the indefinite integral. (Hint: Expand the binomial.) 8. dx 3= 3 +

A:

Q: find inmporopor integreal STæra o dze

A: To solve the improper integral

Q: special fomtion o Show thal (27)

A: We use Gamma function to prove the given result.

Q: Use the form of the definition of the integral in theorem 4 to evaluate the (2x-x') dx HINT: Theorem…

A: we have the integral ∫02(2x-x3)dx  by comparing it with the theorem we get the function…

Q: Fiud the in de finite integrae aud Check the results by A1fferen tiaton. 1

A:

Q: Prove this equa tion analy tic fcz)z Ln /21+iargz Ln 12|+iarg

A: Equation proving in analytical way

Q: Use (3) from Section 5.4 to evaluate the integral. In 6 e* dx =

A:

Q: 10 9. Integrate 4+3cose de.

A: To evaluate the given integral.

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.