Find the exact value of cos20 given sin0 =- and 0 < 0 < 13

Q: Consider the series (In(2n + 1) –- In(2n – 1)). n=1 (a) Let an = In(2n + 1) - In(2n - 1). Does {a}1 ...

A: (a) To check: Whether an=ln(2n+1)-ln(2n-1) Solution: limn→∞ ln2n+1-ln2n-1=limn→∞ ln2n+12n-1         ...

Q: Find a formula for the nth term of the arithmetic sequence. a1= -4, a5=4 an

A: Topic:- sequence and series

Q: Explain why the integral is improper. 81 1 xp 1.4- 1.2- y 0.8- 0.6 0.4 0.2 40 60 80 O At least one o...

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Q: A cylindrical tank with a radius of 5 ft and a height of 20 ft is filled with a certain liquid chemi...

A: topic - application of derivatives

Q: Find the arclength of the curve in the given interval. x = 3 cos? t , y= 3 cost sin t , 0 s<t <t

A: solution is written in below steps.

Q: Differentiate the function. 1,2 g(x) = 6. 6x + 15 | g'(x) = %3D

A: topic - derivative of a function

Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted

Q: Given the following multiplication problem Equation 1: - 24V,=-8V2 -24 8 gives us equations -2 Equat...

A: From the matrix, we have the eigenvalues as  λ1=-26λ2=0 When, λ1=-26 the eigenvector is μ1=-41

Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2.x) b) Fin...

A: Note that, the Maclaurin series of  ln(1-x) is: ln(1-x)=-x-x22-x33-x44-...                  ...(1) w...

Q: dy given that dx Use logarithmic differentiation to find sec-(T) 4sech(5z) (log6 x)" y =

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Q: Determine if f is differentiable at r = 0 given that 4 cos-1 ), if – 2 0, r# 1.

A: The given function,  f(x)=4cos-1x2,if -2≤x&lt;0x3+2πx-16,if x≥0, x≠1

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m³/min. How fast is the...

A: Find your answer below 

Q: Find the slope of the tangent to the curve x^2+3xy+y^2=5 at (1,1).

A: The equation of the curve is given by x2+3xy+y2 = 5                           .......1 The point is ...

Q: Given the triangle below, find sec(0). Enter an exact answer in fraction form. 5 12 13 Provide your ...

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Q: Show the solution that a,+1 < a, for each n E N (-1)" п! n=1

A: Find your answer below 

Q: Evaluate the following integrals (You need to show all your works) Question-1 (. 10 sinx (-2 cosx+2)...

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Q: The monthly costs for a small company to do business has been increasing over time due in part to in...

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Q: Given the following matrix and its eigenvalues -27 3 2 1. Find the two eigenvalues for the matrix 2....

A: a) Eigenvalues: λ1=5λ2=-5 b) Matrix of eigenvalues For λ1=5 -773-3 For λ2=-5 3737  

Q: Given the triangle below, find sec(0). Enter an exact answer in fraction form.

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Q: (금)-(부)' h k Write the equation of the hyperbola in standard form 1 2-

A: Find your answer below 

Q: Suppose that5. an is an infinite Series with Patial Sum 7-2 n:1 16 what are the values of S an and a...

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Q: If y=x^4−5 and dx/dt=−1, find dy/dt at x=−3.

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Q: 6. Find the smallest constantr so that o(x) == x" is a solution to 3z'y" +11lry -3y= 0, for z >0 -3 ...

A: 6.ϕr=xr is a solution to 3x2y''+11xy'-3y=0, for x&gt;0

Q: Question Select your answer. Vhat is the equation of the tangent line to the function F(x) = x? + 2x...

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Q: Find the domain of the rational function. 2x g(x) = (x + 4)(x - 9) {x|x # -4, x * 9, x * -2} all rea...

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Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on t...

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Q: B. Find the sor and aguation of the TANGENT and NORMAL LINE to the curve Graph cach curve, normal, a...

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Q: (b) ) п? + 2n n=1

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Q: Q2/ Sketch each region, label each bounding curve with its equation, and give the coordinates of the...

A: Note : " Since you have posted multiple questions, we will solve first question for you. To get rema...

Q: A spherical balloon is inflated so that its radius (r) increases at a rate of 1/3cm/sec. How fast is...

A: Vloume(V)=43πr3Differentiate w.r.t tdVdt=43π.3r2.drdt

Q: Activity 1 Determine whether the following functions are continuaus or not. If they are not, classif...

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Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 33.2x = y? F...

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Q: onsider the following function. f(t) = 20sqrt t-3 (a) Find the relative rate of change. (b) Evaluate...

A: Consider the following function. f(t) = 20sqrt t-3 (a) Find the relative rate of change. (b) E...

Q: Find the derivative of the function g(x) 3+5x (2), 6 > Next Question

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Q: 1. Express B= 2i +j-3k as the sum of a vect or parallel to A = 3i - j and a vector orthogonal to A. ...

A: To express the vector B→=2i^+j^+3k^ as the sum of a vector to A→=3i^-j^. Solution: let B→=2i^+j^+3k^...

Q: Statement Equation X and inversely as cube of W. z = KM³N the product of r and t and inversely as W ...

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Q: 2. a) Find lim g(x), lim g(x) and lim g(x) 2 b) Find f(1). c) Is g continuous at x = 1? Why or why n...

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Q: y" – 4y' = x2 By used Variation of Parameters Metho

A: Topic:- differential equations

Q: 3x dx - 25

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Q: 1. 3 2 a) Find lim f(x), lim f(x) and lim f(x) b) Find f(1). c) Is f continuous at x = 1? Why or why...

A: We have given figure. And we have discuss about limit and continuity at some certain point. 

Q: (a) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > can is al...

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Q: Question Complete the blank , giving your answers to two decimal places where applicable.(Explain w...

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: 3. Find the constant a so that o(x) = re2 is a solution to y+ay- e =0. 0 4 O 3 0 1

A: ϕ(x)=xe2x is a solution to y'+ay-e2x=0

Q: x = 3 sin 0 is an appropriate trigonometric substitution for the integral 3-x2 dxp. x2 Select one: O...

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Q: Question Select your answer. Find the derivative of f(x) = 5/x with respect to r. 2x 5 Answer

A: Given :f(x)=5xf(x)=x2+5x 

Q: x In(2 + x³) dx

A: Topic  = Integration

Q: If f(x) = 10e" + x°, find f'(x). > Next Question

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Q: Find the equation of the circle that passes through the points (10,2), (9,-3), given that its center...

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Q: A 5 m pole, Teaning against a wall slips in such a way that its base is vedin HOVing away from the w...

A: Draw the diagram and use the Pythagoras theoram and concept of rate of change.