Let {an}, be a sequence of real numbers. Let a2k and a2k–1 be the even and odd terms of this sequence, respectively. Suppose {a2k}=0 and {a2k–1}o converge to the same limit, denoted L. Prove {an}o converges to L. n=0 200 k-1ƒn=0

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: Evaluate the definite integral. n/2 sin*(x) cos(x) dx = -n/2

A:

Q: The region D = {(x, y) : 0 < x < 1, 0 < y <1– x} represents in R?: Select one: A circular region. O…

A:

Q: Answer the following True or False. Let f(x) be a continuous increasing nonnegative function. Then…

A: Let f(x) be a continuous increasing nonnegative function.Then the left endpoint Riemann sum…

Q: Preview Activity 1.1.1. Suppose that the height s of a ball at time t (in seconds) is given in feet…

A:

Q: 3. Given and z2 =? 57 +i sin Z1 where 0se< 2x . 4 = 12 +i sin find cos+i sin 2 37 O 1= 9 cos +isin…

A:

Q: Evaluate the following limit: 2x lim () 14x x00 14x+5 Enter -I if your answer is -o, enter I if your…

A:

Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 3 4 6 2 8 5 7 3 7 2 7 9. (a)…

A:

Q: nd d²x/dt² as a function of if 4 = 7x sin x.

A: Given query is to find the derivative of the the expression.

Q: -) If A and Bare 3 x 3 such that det A = 3 and det B = 2 } Find, if possible, the value of det(A²…

A:

Q: Find the volume if the region bounded above x axis is rotated about the x axis

A: The volume for solid of revolution between curves is the volume of object between a curve fx and a…

Q: 3. Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot…

A: Given: Land in downtown Columbia is valued at $10 a square foot. Triangular lot with sides lengths…

Q: 3. A piece of wire of length shape of an equilateral tr should the wire be cut sa a) a minimum? b) a…

A: L: length of the wirex: one piece of wire cut from length LPerimeter of the equilateral…

Q: Write the partial fraction decomposition of the rational expression. Check your result…

A: We have to write the partial fraction of the rational expression:…

Q: (1) The parts in this question are not related to each other. 4 1 (a) ) Using the e – ổ definition…

A:

Q: Given the triangle below, find the exact value for sec(@). 13 12

A:

Q: dy Consider the differential equation dt = 8y?(y – 1). Use a phase-line analysis to determine…

A:

Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

A:

Q: Exercise 2: Write an inequality or pair of inequalities to describe the possible values of x. Then…

A:

Q: 1) Are the following functions analytic? a) f(z) = z z b) f(z) = z + z?

A:

Q: Integrate the following problems. fe (2x +7)dx 7.

A: Consider the integral  ∫ex2x+7dx

Q: Evaluate the integral using the following values. 8. 8. x dx = 960, х dx %3D 24, 8. dx = 4 4 х dx 4

A:

Q: y-2 z+1 and y +1_2-3 2-3 x+2 v 33.

A:

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A: Total amount of pollutant dumped is obtained by integrating the function A(t)

Q: Find the absolute maximum value of f(a) = x2- 2x +9 over the interval [0,5] The value C for the…

A: Use derivative and integration for the following question.

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: The value C for the solution of the initial value problem f'(x) = x° - 7x + 3, given that f(0) = 0.…

A: Given the initial value problem is f'(x) = x3-7x+3;  f(0)=0

Q: te a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 25…

A: Given query is to find the area of the shaded region.

Q: Find the equation x² + y? + Dx + Ey + F = 0 of the circle that passes through the points. To verify…

A:

Q: Find the limit or show that it does not exist. V1+4x6 (1) lim x- 2- (2) lim (V9x2-5x+3x

A: 1. limx→-∞1+4x62-x32. limx→∞9x2-5x+3x

Q: Sketch the graph of the following function. Describe how the graph can be obtained from the graph of…

A:

Q: Problem2. 3–2x Solve e = 4. And then: 1. Leave your answer in exact value. 2. Round your answer to…

A:

Q: Approximate the area under the curve y = x' from z = 2 to a = 4 using a Right Endpoint approximation…

A: To approximate the area under the curve y=x3 from x=2 to x=4 using a Right Endpoint approximation…

Q: V3x+1(4x+1) (1– 2x)* Calculate y: y=

A:

Q: Find the angles of given that a = 30, b = 14, and c = 19. Round to the nearest tenth of a degree. B…

A:

Q: Solve the system of linear equations and check any solutions algebraically. (If there is no…

A:

Q: Find all possible values of x such that In(x) + In(x + 1) = ln(2). If no such values of x exist,…

A: lnx+lnx+1=ln2

Q: Find the point on the sphere X+y+=4 and the point on The sphere x+y ansi- 2 Selution:-

A: To find the point on the sphere which is farthest from the given  point (1,-1,1).

Q: Suppose that a company makes and sells x phones per week, and the corresponding revenue function is…

A:

Q: 4. The base of a painting on a wall is a feet above the eye of an observer. The vertical side of the…

A:

Q: Consider the geometric series 2n+1 Σ 25 (-3)" n=0 a) I: i What is the first term of the series First…

A:

Q: The entire graph of the function f is given below. Round your answer to the nearest integer, if…

A: Relative maxima is the largest point in interior of the domain.

Q: The function gives the cost to manufacture x items. C(x) = 25,000 + 50x + 800 ; x = 150 Find the…

A: We want to find average cost per unit of manufacturing.

Q: Suppose f(x) > 0 on [0, 3], f(z) <0 on [3,7), f(z f(x) dr = 5, and f(x) dx = -9. Evaluate (0). re…

A:

Q: Assume the point (3,2) is on the graph of y=f(x). Determine the value of n in the following…

A: Given query is to find the value of the indicated points.

Q: Evaluate: (8t3 – 9t2 + 6)dt

A: As per guidelines we can answer only one question at a time so if you need more answer kindly repost…

Q: ,2х 5. e3x.

A:

Q: Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) =…

A:

Q: The value C for the solution of the initial value problem f'(x) = x² – 6x + 2, given that f(0) = 0.…

A: