Solve the initial value problem 8y" - 2y' - y = 0, subject to y(0) = -0.2, y'(0) = -0.325.

Q: Using the graphs of f and g shown below, find the derviative of h(x) = f(x) + g(x) for the domain…

A: The two points on the graph of f(x) on the interval   are:The slope of the line is given by On the…

Q: 2 5. Represent the function as a power series f(x) = o Cnx". Compute the first few 1-7x coefficients…

A: The function 2/(1-7x)

Q: 1) Analyze the function f(x)=x² In(x). Report extrema, inflection points, intervals of monotonicity…

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Q: Determine the amplitude, period, and phase shift for the given function. - cos(2x - 5) y=1- 1…

A: To determine the amplitude, period, and phase shift for the given function.

Q: Simplify the following complex fraction; State the domain restriction: 1 X|N 2 1 1 X 1 -

A: To simplify the following complex fraction. To state the domain restriction.

Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

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Q: Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and…

A: We have to determine the intervals at which the function  is increasing or decreasing.

Q: Find the radius of convergence and the interval of convergence of the series: Σ=1(−1)n+1 +1 (x-2)…

A: The given power series .The aim is to find the radius of convergence and the interval of convergence…

Q: Please answer parts C and D

A: We have to find the limit of the given function.We will use the L Hospital rule to find the limit.

Q: ¡¡¡ ³² 2 cos (x²) 0 0 4у Evaluate the integral 2 cos (x²) 00 4y 5√√Z (Type an exact answer.) -dx dy…

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Q: Compute the electric charge on the surface which is the portion of the cone z = √√3x² + 3y2 in the…

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Q: Evaluate the following limit lim X→∞0 O O O O I 8 0 10/00 8 −5x² +6x³ + 3x² − x 8x² − 2x³ + 3x - 8

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Q: Find the arclength of the curve x = 5t 9, y = 12t – 3 with 2 ≤ t ≤ 5. -

A: x=5t-9y=12t-3

Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

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Q: Find the Maclaurin series of e 00 1 0

A: The given function

Q: n = 1 (-1)"x" n

A: Given that the series we have to find the radius of convergence and interval of convergence

Q: Suppose g is a function which has continuous derivatives, and that g(0) and g"" (0) = 18. What is…

A: Suppose  is a function with continuous derivatives, and that .To find the Taylor polynomial of…

Q: A = 90°, B= 20°, a = 7;

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Q: Compute the surface area of the cap of the sphere x2+y2+z2=49 with 6 ≤ z ≤ 7.

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Q: 19. What is the maximum volume of cylindrical tin can that can be made from 750.0 cm² of metal?

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Q: Perform the following operations and simplify the results. State the domain restriction in each…

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Q: Find the distance d between the complex number - 2 + 4i and 0. d =

A: To find the distance  between the complex number .

Q: Find the derivative of y with respect to x for y = 2*

A: Given that the expression

Q: 9x Find the Maclaurin series of e 10

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Q: mate the average arterial blood pressure over one cardiac cyc

A: We have to find the average blood pressure.

Q: A thermometer reading 8°C is brought into a room with a constant temperature of 28°C. If the…

A: A thermometer reading 8C is brought into a room with a constant temperature of 28C. If the…

Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: f(x) = ln(x)

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: Find the equation of the tangent to the curve cos²x - sin²x y = at the point where x = I |4

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Q: 17. Suppose you want to fence three sides of rectangular region where one side is bordered by a…

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Q: j. lim sin x x →0 k. lim sin² x x→0 1. lim sin 3x X-Z 2 m. lim cos³ x X→= 2

A: To find:-(j) (k) (i) (m)

Q: Find the absolute minimum and absolute maximum of f(x, y) = 192x³ + y²(1 - 4x) on the triangle with…

A: Given function is Now, we have to find the absolute minimum and absolute maximum for the above…

Q: 2x³+x²+x+1 x→∞0 4x³-x²-8 √x²+x+1 lim x→∞ √4x²+3 k. lim 1.

A: K) limx-infinity (2x3+x2+x+1)/(4x3-x2-8)I) limx-infinity +x+1)/sqrt(4x2+3)

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A: Let the diameter of semicircle be x feetThen radius of semicircle be  feet

Q: (d) lim Bl x-l lnx (e) lim x-x)

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Q: Determine whether the graph is that of a function. If it is, use the graph to find its domain and…

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Q: Approximate the area under the graph of ?(?)=4−?^2 with 4  equal subintervals from ?=−2 to ?=2 using…

A: The objective of this question is to approximate the area under the curve of the function f(x) = 4 -…

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: se the given information to evaluate each expression. (Enter your answers in exact form.) sin a =…

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Q: f(x) = -2(sin(3x + pi/2)) + 1 for x is an element of [0, 4pi/3] State the phase shift, period,…

A: The given function is  , The standard equation of Amplitude Phase shiftVertical shiftTime period

Q: √x 4√/2x+1dx X

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Q: Suppose limx→cf(x) = 5 and limx→cg(x) = -2. Find: a. limx→cf(x)g(x) b. limx→c2f (x) g(x) c. limx→c…

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Q: Find the points on the curve x = t² - 16t – 5, y = t² + 14t + 7 that have: A. a horizontal tangent…

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Q: Estimate the average value of f(x) from x = a to x = b. 28 21 f(x)

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Q: The Taylor series for f(x) = x³ at-4 is cn(x + 4)". Find the first few coefficients. Co= C1 = C2 -…

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Q: You are playing on the beach with your dog, Ohana. You throw the ball into the water at a point that…

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Q: = Find fæ, fy, fxx, fyy, fay for the function f 5 x³ siny+8 y² cosx+3x+7y.

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Q: 16. Split the number 15 into two parts so that the product of one part and the other is maximized.

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Q: Suppose that we're making and selling some widget and the cost (in dollars) when making a widgets is…

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Q: Find the point on the curve e +x where the tangent is parallel to the line y = x.

A: The given equation of the curve is  and the equation of the tangent line is