Is the series convergent or divergent? If convergent, is it absolutely convergent? cos (πn) e-n COS Σ n=1

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: Order is the highest power of the derivative Degree is the power on the highest power of the…

Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

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Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O-4 and 2…

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Q: 11. Identify the horizontal asymptote of * 3 f(x) = +2 x-2 Oy=1 Oy=2 y=3 Oy=-2 Identify the domain…

A: Horizontal asymptote:If  then the line y=L is the horizontal asymptote of the function f(x)

Q: Express 0.132 as a geometric series

A: The given number .The aim is to write the number as a geometric series.

Q: Evaluate the following integral. 36 2 x - 36 36 x²-36 2 dx= dx

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Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

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Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 11.…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

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Q: 7. 10 Consider the function f and the point Po given below. Find a unit vector u in the direction in…

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Q: he graph of the derivative g' has exactly two roots. Complete parts a through c. OB. There are no…

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Q: differentiate y(theta) = e^cot theta

A: given function

Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: Use spherical coordinates. Evaluate JJJ y²z² dv, where E lies above the cone 4 = 1/3 and below the…

A: G

Q: Evaluate the following limit. lim x³e -x² xxx = Note: Input DNE, infinity, and -infinity for does…

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Q: Find the inflection points of thefunction f(x) = e(79-x²). INTERMEDIATE WORK f'(x) = f"(x) = On what…

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Q: If C(x) is the cost of manufacturing an amount x of a given product and $10 is the price per unit…

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Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete 3. (x²y + 2xy² -…

A: The given differential equation

Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: The indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4+x² - y2…

A: The given function  and region R

Q: Consider the function F(x, y) = xy2 + 2xy-6y2-8x-12 y + 54. (a) Find the critical points, where Fx…

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Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to find the given function as a composition of two functions f and g.

Q: In 1994, the moose population in a park was measured to be 4460. By 1997, the population was…

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Q: 1 Let f(0)= sin(0) + cos(0). √√3 Calculate the derivative. [Note: to get the to show up type theta,…

A: Consider the function

Q: Evaluate the following limit. lim 8+←8 15 ln x X = Note: Input DNE, infinity, and -infinity for does…

A: Given,

Q: Find aw/as and aw/ât using the appropriate Chain Rule. Values Function w = y³ - 2x²y x = es, y =et S…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The equation of the curve is given byTo determine: The slope of the tangent line to the given curve…

Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: Evaluate the double integral [[ (zy + 2) dA, where D is the set of points contain within the corner…

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Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: ROBLEM No. 1. Solve the IVP: y"+6y-7y=0, subject to the initial conditions: y(0)=5; y '(0)= -3.

A: Given Differential equation is as follows

Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: (1) (2 cos y + 4x²)dx = xsin ydy

A: given differential equation

Q: Evaluate the integral by converting to polar coordinates. 3 S³ S 0 9-x² cos(x² + y²) dy dx = 0

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Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

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Q: Find the derivative  a. y= ln(cos^2x) b. y= e^cosx+e^-x

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Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: At what point(s) on the curve x = 6t² + 9, y = t³ - 5 does the tangent line have slope 2 (x, y) =

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Q: If what does the following integral equal? 4 19 q(s)ds = [ q(s)ds = 13 and La q(s)ds = 10.7

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Q: (4) y' + (x + 1)y = ex²y3

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Consider the sequence

Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete solutions. 2.…

A: To solve the following differential equation by using Homogeneous DE.

Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

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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: What is the unit tangent vector T(t) on the curve r(t) = (sin(t), 3, 2 cos (2t)) when t = 0? Select…

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Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ''(x)(x − b)dx a

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Q: 1 V₁ V2 = 2(+/-+- (1 (v₁/v₂) = 2 sin = -2V²-V²_2₁ Z₁ cos 1 =2²₁√√√√²₁ X Z₁ + V/₂ √/1-(V₁/V₂)² V₂ V2…

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Q: Find the area of the region enclosed by y=4.75x and x = 9 - y². 2 on 5 6 7 00 a Use horizontal…

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