Determine if the geometric series converges or diverges. If it converges, find its sum. 3 8 0·00 + + ... + 9 8 8 1+-+ 9 9 2 8 9 n + ...

Q: 1 3 2 1 a To find the blue shaded area above, we would calculate: ·b [ f(x) dx = area Where: f(x) =…

A: The given graph

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Q: 2. Differentiate the following functions. a. b. Differentiate the following function. f(x) = 775…

A: (a) f(x)=7π6

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A: y=limθ→π2−(15tan⁡θ)15cos⁡θ

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A: Rewriting expression

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A: Given: To Find: (a) To find the linear approximation for the given function at the given point.(b)…

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A: Given that the vertical asymptotes are  and x intercepts are  and horizontal asymptote is

Q: (c) f(x) = (52–6)* 3x²+4 Solution: For this one we need to use the quotient rule first.

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Q: 3. Consider the curve which is the graph of the equation r³+y³ - 3xy = 0. Graph this curve using…

A: In this question, we will find the implicit derivative.

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Consider the following. 8n 77 Calculate, to four decimal places, the first ten terms of the sequence…

A: The sequence is given by :-

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Q: Differentiate +6) In (3x5 + 11x³ +

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Q: Describe verbally the transformations that can be used to obtain the graph of g from the graph of f.…

A: we are given two functions, we need to write down the transformation that f(x) should undergo in…

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A: Given:To Find:  (a)  To find the initial area of the sector.(b) To determine the rate of change of…

Q: Let g(x) = ² + 12 Ax² + B (x²+12) C A = B = C= = D = E = F = g"(x) = x(x² + E), where (+²+F)G where…

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Q: Derivative Rules: 1. Power Rule: (2”) = n d dx Special Case of this: (√T) 4. Quotient Rule: (²) ₁- V…

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Q: Find the derivative a. f(x)= (e2x+e)1/2 b. f(x)= ex(x2+3)(x3+4)

A: (a)  given,

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A: The tangent to a curve at a point is obtained by finding the slope at that particular point using…

Q: Find a formula for the nth term of the sequence below. -6, 6, -6, 6, -6, ... Choose the correct…

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Q: Find all the second-order partial derivatives of the following function. W = 3x - 2y 2x² + 3y

A: The given function is

Q: Practice 2: Suppose that f(2)=-3, g(2)=4, f(2)=-2, and g (2) =7. h(x) = f(x) g(x)+5g(x)- 100 Find…

A: f(2)=-3, g(2)=4, f'(2)=-2, g'(2)=7h(x)=f(x)g(x)+5g(x)-100Find h'(2).

Q: Find the location of the maxima, minima, and saddle points of f(x,y), if any, given the partial…

A: The given first order partial derivatives are

Q: 4. Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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Q: Use Trigonometry Substitution to evaluate the following integral. / 3 = 273d² -dx

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Q: Find the derivative a. f(x)= 6/(3x2-pi)4 b. f(x)=((3x2-pi x)4

A: (a) given,

Q: SS (3X-5) dA; R is R Eval & Reverse ? Triangular Region bounded b y=x+5 Y=-X+7 X=10

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Q: 7. 1 Suppose f (x) is a continuous function and 0 < f (x) < ². Does ₁° f (x) dx converge or diverge?…

A: If f(x) is continuous then we can integrate between some limits.

Q: The edge of a cube was found to be 11 cm with a possible error in measurement of 0.81 cm. Use…

A: Let the edge of the cube = x

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A: Consider the figure

Q: Suppose that 3 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: Consider the following. A = Convert the iterated integral to polar coordinates. A B S^L. ( Jo Jo B =…

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Q: Differentiate In (5x² +1) 6x³ + 1

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Q: 2. Addition/Subtraction Rule: (uv)'=u'±v' 3. Product Rule: (uv)'= u'v+uv' u'v - uv (+)'-*'-we 4.…

A: p=(q+2)/(3q-1)

Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

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Q: Seperate the variables and solve the equation (dy/dx)=-e^(x-y). Use the initial condition x=0; y=0…

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Q: Find the derivative of the function. y = sin() + sin (9 x) y'(x) = ||

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Q: Find the value of an investment of $20,000 for 14 years at an annual interest rate of 3.85%…

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Q: Show the limit x³ y lim (x,y) →(0,0) x6 + y²

A: L=lim(x,y)→(0,0)x3yx6+y2

Q: Find the surface area of revolution about the x-axis of y = 72 + 6 over the interval 2 ≤ ≤ 5

A: The given equation is  over the interval..Calculate the surface area of revolution about the…

Q: (a) Consider the curve y = e dx 6x + 6). (c) This function is always differentiable. Its derivative…

A: Consider the curve (a) To find (c) To find the values of  when .(d) To find the intervals where the…

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

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