.2 x²+1 lim x-∞ x²-1 X-

Q: Sketch the graph of ONE function that satisfies, ALL of the following conditions. Label ALL…

A: The given condition to draw a graph of function

Q: 1 Assume that f'(4) = -5, g'(2), g(2)=4, and y=f(g(x)). What is y' at x = 2? 8 Atx=2, y'= (Simplify…

A: The chain rule of differentiation is given by

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: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of…

A: Length of box=x feetWidth of the box=x feetHeight of the box=y feet The figure

Q: the following operations and simplify the results. State the domain restriction in +5x-14 2+8x+7 ÷…

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Q: Use the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms.…

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Q: Solve the following initial value problem. f(0) = 2 500. f'(x)=√x+x²,

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

A: Given that the expression

Q: dx Assume that x = x(t) and y = y(t). Let y = x + 2 and dt dy Find when x = 3. dt dy dt (Simplify…

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Q: Find the first few terms of the Taylor series centered at x = 0 to evaluate: COS 1 lim I→0 x²

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Q: Find the exact value of each of the following under the given conditions. 6√85 85 5 sin a = 13 (a)…

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Q: The cost of laying a fibre optic cable underwater is 3 times that of underground. An island is 4 km…

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Q: Use the information given below to find sin(a-B). tan a = with a in quadrant 1 12 5' sinB =15, with…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Use the method of substitution to evaluate each of the following general antiderivatives. 6x² (b)…

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Q: Evaluate the integral: · √2 9 1 + x² -dx

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Q: n -Σ„² n=0 If f(x)= = n -x" and g(x) = (-1)"- n² +1 n n² + 1 n=0 -a", find the power series of + 1/…

A: f(x)=∑n=0∞nn2+1xn and g(x)=∑n=0∞(−1)nnn2+1xn,

Q: 5. Solve y"" - 6y" + 11y' - 6y = 0

A: The given differential equation is

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: The function f(x) = x 4 has a Taylor series at a = 1. Find the first 4 nonzero terms in the series,…

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Q: Let f(t) be the function 2t² + 1t+5. Follow the steps below to use the formal definition of the…

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Q: 10. Consider the following two 3 x 3 matrices -1 3 3 1 -2 -1 1 -2 -2 (b) ( (c) A = 1 1 AB and BA. (…

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Q: If sin(-s) = 5/13, and (a) (b) (c) (d) sin s cos(-s) COS S 3πt < s < 2π, compute the following.…

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Q: Given the following data points, fill in the estimates of the integral that each method predict (use…

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Q: height (feet) of an object moving vertically is given by s= - 16t² +288t+216, where t is in seconds.…

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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: 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: A rectangle has its base on the x−axis and its upper vertices on the parabola y = 9−x^2. Find the…

A: Given that a rectangle has its base on the x−axis and its upper vertices on the parabola To…

Q: derivative In 2 x-1 2 x+1

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Q: 5. Calculate the following limits: x-5 a. lim x-5x2–25 b. c. d. lim x--5 x²+3x-10 x+5 t² +t-2 lim…

A: 5)a) limx-5 (x-5)/(x2 -25)b) limx-(-5) (x2 +3x-10)/(x+5)c) limt-1 (t2 +t-2)/(t2 -1)d) limx-(-2)

Q: Find the area of the region that lies above the x-axis, below the curve x = =t² + 5t+3, y = e with 0…

A: Given that the region that lies above the x axis, below the curve  with

Q: Find the general Solution For D-E x dy dx +y = !

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Q: 20. What value of x will give the maximum efficiency of a screw with a coefficient of x-μx² friction…

A: Given that, a friction coefficient  .We need to obtain the value of x for which we get the maximum…

Q: ↑ X The amount of plutonium remaining from 1 kilogram after x years is given by the function W(x) =…

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Q: Find a function ?(?) such that ?′(?)=?^x+?^e+1

A: The objective of the question is to find the antiderivative or integral of the given function f'(x)…

Q: The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t) =…

A: The amount of carbon-14 present in animal bones t years after the animal's death is given…

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: 9x Find the Maclaurin series of e 10

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Q: Solve the initial value problem If the solution is y = co + C₁x + ₂x² + C3x³ + C4x² + C5x5 +C6x6 +…

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Q: Find an equation in rectangular coordinates for the spherical equation p = 4 sec (6)

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Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

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Q: x²+3x-130 lim 2 x-10 x²-100

A: L=limx→10x2+3x−130x2−100

Q: A cone is designed to have a radius of 6 cm and a height of 9 cm, but the radius and height are off…

A: Radius= 6 cmHeight= 9 cmChange in radius is 0.03Change in height is -0.06

Q: When a circular plate of metal is heated in an oven, it’s radius increases at a rate of 0.05 cm/min.…

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Q: 3. Sketch these functions and find their domain and range. a) f(x) = √√3x b) y = x³

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Q: Find the equations of the tangent and normal lines to the graph of the function at the given point.…

A: The equation of the tangent line  to the curve y= f(x) at x= a is  The equation of the normal line…

Q: Determine the amplitude, midline, period, and an equation involving the sine function for the graph…

A: A graph of the trigonometric function is given.The aim is to find the equation of the graph.

Q: 1. Describe the convergence of the series 3! + 3² + + (n+1)² (n + 2)! +

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Q: For 0 ≤ t ≤ 30, the rate of change of the number of mosquitoes on Tropical Island at time t days is…

A: The objective of this question is to find the number of mosquitoes on Tropical Island at time t=30…

Q: Graph the function for one period. =tan(лx/2) for 0.5 1.0 1.5 y y-intercept 1.0 vertical asymptotes…

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