Use the formula for the binomial series: (1+x)™ = m(m-1) x²+ 2! m(m–1)--(m-k+l),k + 1+ mx + + ... ... k! m(m-1)..(m-k+1) 1+ Ek=1 x if |x| < 1 k! to obtain the Maclaurin series for V1+ x. 1 1-r + S(-1)°• 13 · 20…(7k – 8) 7* k! k=2 00 1+r+ S(-1)k+1© • 13 · 20…(7k – 8) 1 + x + 7k k! k=2 13 · 20...(7k – 8) 1+ E(-1)*13 - 7k k! k=1 13 · 20..(7k – 8) 1 + k! k=1

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about a = x0 and then find the nth Taylo...

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Q: C. Determine the value of a and b that make the given function continuous. (Choose one) ax + b x1 ах...

A: Topic:-  limits and continuity

Q: (sin y – y sin x) dx + (cos x + x cos y – y) dy = 0

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Q: 1 1 f(x,y) = x² - 2xy + 3x +y? %3D 1. Compute the first- and second-order partial derivatives. 2. Fi...

A: Solution is given below:

Q: 9. Given the vector ū =[-2,3,–4] a) Draw the vector. b) Determine a unit vector collinear with ū. y

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Q: What is the volume of the solid generated by revolving the shaded region about the line y = 3 y x = ...

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Q: The angle of rotation is 18.485 of the conic section with equation Ax-Bxy +Cy 4, if A- C- 20 and B+ ...

A: Angel of rotation

Q: A group of workers can plant at a rate of  10  acres per day. How many acres can they plant in  5 ...

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Q: dy/dx = 8y-1 a, Solve with separation of variables method b, Solve by integrating factor method c...

A: topic -  differential equation

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at a = 8 for f(x) = In(x +1). %3D

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Q: A is an m x n matrix. Check the true statements below: A. The column space of A is the range of the ...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: ∑n=0∞ (-1)n+1 (n+4) xnan = (-1)n+1 (n+4) xn   limn→∞ an+1an &lt; 1limn→∞ (-1)n+2(n+5)xn+1(-1)n+1(n+4...

Q: Use inductive reasoning to predict the most probable next number in the given sequence: 1, 7, 17, 31...

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Q: Activity 3.2. Find the slope of the tangent line to the graph of the function defined by y = 4 + 2x ...

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Q: 1. A soccer ball is kicked 20m/s at an angle of 30° above the horizontal. Determine the horizontal a...

A: Using trigonometric find horizontal and vertical components

Q: 3 Find the average rate of change of g(x) = 8x² + on the interval [-3,2] x3

A: topic -   average

Q: Lesson 3.1. Slope of a Tangent Line to a Curve Activity 3.1. Find the general equation of the slope ...

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask th...

Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative. 

Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+x 1 F(x) = 1 +x+ :·...

A: Using the binomial series expansion: (1+x)k=1+kx+k(k-1)2!x2+k(k-1)(k-2)3!x3+...                     ...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 3 %3D P4(x) ...

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Q: d'y Find dz? of the function given implicitly: 6xy + 7e = 7e.

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Q: Given: (-8, 6) cote = -3/4 O 4/3

A: Find your answer below 

Q: Using the figure shown, find sing (3, - 4) -3/5 3/5 4/5 -4/5

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Q: If a force of 60 lb. acts at an angle of 40 to the horizontal, what is its vertical component? 39 l...

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Q: For the following function, a) give the coordinates of any critical points and classify each point a...

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Q: Find the derivative of the function. f(t) = 8r2/3 - 4t/3 + 8 f (t)=

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Q: From a window, the angle of elevation of the top of a flagpole is 25, and the angle of depression of...

A: upper triangle make 25' with top of flagpole so now using trigonometry use tan25 = (flagpole length ...

Q: I need help with the red questions below

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Q: Sum and Difference Rule of Differentiation. Give 3 examples with solution and final answer. Make sur...

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Q: A region bounded by the following curves is revolved around the y-axis. Use cylindrical shells to fi...

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Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

A: Question - a Given functions, x=y2x=2-y2 Axis of rotation, y=1 Formulas used: ∫xndx=xn+1n+1

Q: You are given the graph of a function f defined on the indicated Interval. Find the coordinates of t...

A: Absolute Maximum of a Graph: The absolute maximum of a given graph is the point on the entire graph ...

Q: Y zo when X-0 -h sin TRX

A: topic - integration 

Q: The quantity of a drug, Q mg, present in the body t hours after an injection of the drug is given is...

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Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

A: As per guidelines I can only solve first three subparts , remaining can be reposted

Q: Find the radius of convergence and the interval of convergence. k(k + 1) k=1

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Q: Max bought a new video game that was on sale for 25% off. If the regular price of the video game was...

A: Topic = Algebra

Q: A. Find the derivatives of the following functions: 1. f(x) = (-x - 5)* 2. f(x) = (-x² - 4)-2

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Q: Determine whether the series is convegent or divergent. If it is Convergent, find its Sum, 8) nニ2

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Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

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Q: Find the indefinite integral. (Use C for the constant of integration.) 5 cosh(/x) xp

A: ∫5cosh(x)xdxlet x=tdifferentiate on both sides12xdx=dtThen ∫5cosh(x)xdx=5∫2cosh(t)dt

Q: Given f''(x)=−9sin(3x) and f'(0)=4 and f(0)=−1.   Find f(π/4)=

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Q: 12. Simplify the following rational expression for the function f (x) = 5x2 f(x + h) – f(x) h

A: Given f(x)= 5x² So, f(x+h)= 5(x+h)²=5x²+10xh+5h²  

Q: 4 + sin(n) n2 00

A: The given series,         ∑n=1∞4+sin(n)n2

Q: Find $Y if y = x-3 x -7 ond X=2++1 %3D

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Q: Question 3: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x)...

A: The given function,    fx=x2-2

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: The given sequence,      17, 179, 1792, 1793,......

Q: For f(x)=(x^2+x−2)/(x+2) does the Mean Value Theorem apply on the interval [0, 2] and why?

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Q: For f(x)=√(x^2+2) find all the values of c on the interval [0, 1] that satisfy the Mean Value Theore...

A: Given query is to apply mean value of theorem and find value of c