What is a monotonic sequence?

Q: Proving a Sequence Is Geometric Show that 3, 6i, – 12, -24i, ... is a geometric sequence, and find t...

A: Concept,If a series is given as - a, b, c, d, e, .........Then series is said to be geometric sequen...

Q: What present value P amounts to $300,000 if it is invested at 8%, compounded semiannually, for 18 ye...

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Q: 3.

A: Given: (a) 73(b) 74   

Q: need help on this question

A: The given function is, f(x)=4x2+8x The interval is [-1,1] that is, -1,-35,-35,-15,-,15,15,15,35,35,1...

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

A: Given function: f(x,y)=6-x4+2x2-y2 First, find the first partial derivatives fx and fy : fx=∂f(x,y)∂...

Q: a. Find the derivative of f at x. That is, find f'(x). b. Find the slope of the tangent line to the ...

A: Slope of tangent is given by placing the given point in the first derivative of f(x).

Q: Consider the region in the first quadrant, bounded by the curves y=x^3, y=x^(1/2). For each of the f...

A: Given curves are y=x3y=x  

Q: Find the volume of the region bounded below by the paraboloid z = x2 + y2, laterally by the cylinder...

A: Find the volume of the region boundedbelow by the paraboloid z = x2 + y2, laterally by the cylinderx...

Q: Find the arc-length from (-3,4) clockwise to (4,3) along the circle x^(2)+y^(2)=25. Show that the re...

A: Given: x2+y2=25 now, for finding arc-length from -3,4 clockwise to 4,3 along the given curve, first ...

Q: sec² (x) tan° (x)dx

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Q: 1 Evaluate dx dy. JO 1+ 2x + x2

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Q: Explain why the sine or cosine of an acute angle cannot be greater than or equal to 1.

A: Let us consider a right angled triangle as below. Here θ is an acute angle. In the right angled tri...

Q: Polar coordinates of a point are given (8.3, 4.6). Find the rectangular coordinates of each point.

A: r, θ=8.3, 4.6⇒r=8.3 & θ=4.6

Q: Please read each statement below very carefully. Which of the following statements about the central...

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Q: The rate of U.S. per capita sales of bottled water for the period 2007–2014 could be approximated by...

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Q: Evaluate the function at the given values of the independent variables. = x³ + 3xy + y²; x = -1, y =...

A: z=x3+3xy+y2x=-1  and y=1 Replace the x  and y values in the given function  

Q: a. Approximate the given quantity using Taylor polynomials with n= 3. b. Compute the absolute error ...

A: Given: cos(0.24)

Q: Find the end points of the minor and major axis for the graph of the ellipse (z - 5). (y - 7) + :1 1...

A: Given Equation of the ellipse  x-5216+y-7236 = 1   Compairing it  with general equation of the ellip...

Q: 1. Find the equation of the tangent line to the curve defined by the equation In(xy) + 2x – y + 1 = ...

A: Given: lnxy+2x-y+1=0 for finding equation of tangent at point12,2, we need to find slopem of tangent...

Q: Which of the following sequences is an arithmetic sequence? Select all correct answers. Select all t...

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Q: A concert promoter needs to make $84 comma 000 from the sale of 2400 tickets. The promoter charges $...

A: Word problem of equation: A concert promoter needs to make $84000 from the sale of 2400 tickets. The...

Q: Graph the absolute value function,f(x) = | x| . Then use transformations of this graph to graph the ...

A: the given function is f(x)=x. we have to graph the function f(x). then we have to use the transforma...

Q: scribe how the graph of b is kept constant and

A: Hyperbola: The equation of hyperbola isy2a2-x2b2=1 a. We need to find relation between x,y and b whe...

Q: Evaluate the integral or show that it is divergent.

A: ∫dx4x2+4x+5=∫dx2x+12+4=∫dx2x+12+22=12tan-12x+122+C    ∵∫dxx2+a2=1atan-1xa+C & x-coefficient must...

Q: Evaluate each definite integralusing the Fundamental Theorem of Calculus

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Q: 1 Find the exact value of cos(20) if sin(0) O 3 7 9. /3 3 1/9

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Q: for the question i got -1/8, Where did i go wrong?

A: f-1'(a)=1f'f-1(a)

Q: The derivative of a function f(x) is given by f'(x) = (x – 2)(x +4) Va2 + 1. a. Find an equation for...

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Q: The volume of the sphere is 36 π cm3.Find the surface area of the sphere ,correct to the nearest

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Q: Evaluate each definite integralusing the Fundamental Theorem of Calculus

A: The given expression is, I=∫0π4sec2θdθ Consider that the integral of sec2x is tanx and the. Then, so...

Q: Find the exact value of the expression csc 37° sec 53° - tan 53° cot 37°.Do not use a calculator.

A: Let the given expression be y - y = cosec37°sec53° - tan53°cot37°y = cosec90-53sec53 - tan53cot90-53...

Q: Find the arc length of the graph of y = √(16 − x2) over the interval [0, 4].

A: Given: y=16-x2 interval [0, 4]

Q: Compute the following derivative, where A, B, C, D, and E are all functions of the variable x. Inclu...

A: ddx7+B+9ACE-5D

Q: A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. Is A diagonalizable? Why...

A: Given that A is a 3*3 matrix with two Eigen values Have to state whether it is diagonizable or not.

Q: Among all rectangular regions 0 ≤ x ≤ a, 0 ≤ y ≤ b, find the one for which the total outward flux of...

A: Given force - F = x2+4xyi-6yjFlux is given by = ∮F.dAwhere, A is the area.dA = dxdyLimits for x,    ...

Q: Given a(t)=<4t,6t,1>, v(0)=<1,-1,1> and r(0)=<1,0,0>, find v(t) and r(t).

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Q: Note: Solve only points a, b and c.   Consider the graph of the derivative of a function f, given be...

A: For a function f(x) , first derivative f'(x) is used to find the critical points. Critical points ar...

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.