Determine the limit of the following: 1.1) lim x -->3 (sqrt 3x / x sqrt x + 1) 1.2) lim --> pi / 3 (sin 2x / sin x)

Q: Evaluate; In (sin²s ) sin2xdx sinx +C 3 A sin?x B) +C sin

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Q: E. Discuss the continuity of the function g(x) = on the interval (0,2] and [-1,3]. x2-4

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Q: -7. -5-4 -3-2 -1 \I 2 3 4 5 -2 -4- o ト oゆ!

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. (Hint: factor the den...

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Q: 2 Find all local extreme values of f(x) = a 3 5x2 + 8x – 50. The FIRST local extreme value, moving f...

A: topic- application of derivatives

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Q: Complete the following table. 2 x2 ±1 +0.5 +0.1 +0.01

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Q: 3. Find the solution to the initial value problem y'+ y = 12t, y(1) = 6. 4t3

A: This question is related to differential equations, we will solve it using given information. 

Q: Write an equation for the line parallel to y : – 3x + 3 and passing through the point (4,-16) y =

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Q: d. One focus at (-3 - 3v13,1), asymptotes intersecting at (-3,1), and one asymptote passing through ...

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Q: Calculate the iterated integral. '1 I l'x+e-Y) dx dy Need Help? Read It

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Q: 100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the ro...

A: Theorem : If the series ∑n=1∞|an| converges, then the series ∑n=1∞an also converges.                ...

Q: 181?action=Donresume&submissi G(x) = tan t dt. %3D G (1)=| G' (0) %3D G' (주) =

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Q: The polar coordinates of a point are given. Plot the point. (9. ) n/2 10 7/2 10- 5 -5 -5 -5 - 10 T/2...

A: Consider the polar coordinate  9,5π4

Q: Suppose f'(x) is continuous over an interval a < a < b, and a <c <d < b. If f'(c) = 9, then (check a...

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Q: in yy = 2 y-x; %3D

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Q: Determine whether the series converges using any appropriate test. Identify the test for convergence...

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Q: [1 23 A 3 4 5] Given matrix A above, in the matrix multiplication: IxA = A.What is matrix To create ...

A: Find your answer below 

Q: 1 Use the trapezoid rule and Simpson's rule to approximate the value of da with n = 4. 9 + x3 Note t...

A: Trapezoidal Rule :         ∫ab f(x) dx ≈ ∆x2f(x0)+2f(x1) + 2fx2+...+2fxn-1+fxnwhere , ∆x = b-anSimps...

Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y) = y² – x² sub...

A: Let's find. 

Q: 1. (a) Find the first four nonzero terms of the Taylor Series for the given function centered at a +...

A: i) f(x)=ex , a=ln 4ii) fx=ln x, a=3

Q: | sin x (3cos*)dx 2:

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Q: As you know, when a course ends, students start to forget the material they have learned. One model ...

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

Q: The integral dx is Select one: O None. o o o

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Q: Find the arc length of the curve x = –3y3/2 from y = 0 to y = 10. Length =

A: To find the arc-length if the curve x=-3y32 from y=0 to y=10 Now, the formula for the arc-length is:...

Q: An object is dropped from a height of 124 feet. ti = 0, t2 = 2 (a) Use the position equation s = -16...

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Q: For a survey, students were assigned to either Ror group V. Combined, the students in both groups an...

A: Given problem:- For a survey, students were assigned to either group R or group V. Combined, the stu...

Q: Determine whether the series converges using any appropriate test. Identify the test for convergence...

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Q: e" dx Find (ez +3)(e –5) Find S In(x)x²dx.

A: The first question can be solved using the concept of partial fraction and the second question can b...

Q: 1 The region bounded by the graph of f(x) and the x-axis between x = 0 and x = 9 %3D 1+ x2 is revolv...

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Q: Problem: Find the answer following of the alittrential equation. d=2 tan(a) Secix) -y"sinca)

A: Given:    y'=2 tanxsecx-y2 sinx

Q: Evaluate the iterated integral. 3 4 y+5y) dx dy 10

A: The given integral,      ∫13∫04x3y+5y dx dy

Q: Which of the following is/are the point/s of discontinuity of the function whose graph is shown belo...

A: The given question can be solved as shown instep2.

Q: dx 1+ x2/3

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Q: Calculate the Taylor polynomials T;(x) and T3(x) centered at a = 8 for f(x) = In(x + 1).

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Q: dy x + y ; 4- dx 2xy ls

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Q: Let f(x) = ln(2x). Note that 1 and 2 can be done at the same time if your answers are in table forma...

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Q: -5 -4 -3 -2 -1 2 3 4 5 -1 -3 17x the above rational function f( x ) = identify its three infle 1.5x2...

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Q: Before starting your studies at EHL, you need to buy new suits. Each suit is made of a jacket, a tro...

A: According to given, Total purchase= 450+560+180+240+290+85+89+96+92= 2082 Since the purchase price &...

Q: An inverted conical water tank with a height of 12 ft and a radius of 6 ft is drained through a hole...

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Q: An object is dropped from a height of 124 feet. t1 = 0, t2 = 2 (a) Use the position equation s = −16...

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 ft/min, and its coarseness is such that ...

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. Зд 2 = sin...

A: topic - sequence and series

Q: Calculus Question

A: Perform integration

Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², (2x + k,...

A: Answer: The solution is as given below:

Q: The integral of any quotient whose numerator is the differential of the denominator is the LOGARITHM...

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Q: (a) Let m and n be positive integers. Show that T if m = n, sin mæ sin næ dx 0 if m + n.

A: We know  Sin^2x= (1-cos2x)/2  

Q: Find the value of a that will make the function continuous at every real number. x*, f(x) = {ax? + a...

A: We have to find the value of a that will make the function continuous at every real number.         ...

Q: Evaluate: / 3'/ | 3° +4dy A 3' +4) : In27 +C A 2 (3+4) +C B.

A: Integration