At what points is the function y = X+5 - 8x + 15 x²- continuous? Describe the set of x-values where the function is continuous, using interval notation. (Simplify your answer. Type your answer in interval notation.)

Q: 3. Use the definition of Taylor series to find the Taylor series centered at a = 1 for f(x) = ln x

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Q: 11. A farmer wants to fence off a rectangular plot of ground with area 3000 ft² and divide the plot…

A: A farmer wants to fence off a rectangular plot of ground with area 3000 ft2 and divide the plot into…

Q: If ſ²₁ f (x) dx = 3 and ²₁ g(x)dx = 8, find §²₁₂[4ƒ(x) — 2g(x)]dx -1 -1

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Q: Given the geometric sequence: 20 3 find a formula for the n-th term: ao = 2, a₁ a1 = , a2 = 200 9…

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Q: Estimate the area under the graph of f(x) = 3x³ between x = 0 and x=4 using each finite…

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Q: Σ(17)

A: ∑n=1∞(3n+7n11n)

Q: x³ + 3x² = 1 3

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Q: f(x) = −x+10 g(x) = x² − x − 11

A: Given that the function

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A: Given that the expression

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: The approximate rate of change in the number of design patent applications received in recent years…

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Q: Find the tangent to y =√x-x+10 at x = 10.

A: y=x2−x+10 at x=10dydx=ddxx2−x+10Chain Ruleddxf(g(x))=f′(g(x))g′(x)Using the power Ruleddxxn=nxn−1

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: A circle has an initial radius of 50 ftThe radius begins decreasing at the rate of 5 ​ft/min

Q: 21. A window is composed of a rectangle with a semicircle above. If the perimeter is 16.0 m, what…

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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: A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min ​(see…

A: The hemispherical tank of radius

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

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Q: The function y(x) saifies the following equation: Find an expression for dy dx 5 x² − 2xy+3y² − 3 x…

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Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: cos(x) - 1 lim 10 esin(z)-1-x

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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: The population of the world¹ t years after 2010 is predicted to be P = Round your answers to one…

A: To find the population in 2026 and the average population between 2010 and 2026.

Q: 4. The financial department of a hospital arrived at the cost function: C(x)=20x³-360x² +2300x-1000,…

A: Given cost function is

Q: Suppose that we're setting up a wireless data network for a small municipality. The local ISP wants…

A: The given cost function is

Q: 17. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed…

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Q: Take the logarithm of both sides of the equation and expand it using the product rule of logarithms…

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Q: 3√2 2 [*** 9-x -x² - y² e Evaluate the integral 0 using cylindrical coordinates. Enter an exact…

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Q: Suppose that the radius of convergence of the power series   cn xn is R.     What is the radius of…

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Q: nn n=0 4"n! η!

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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: Find the surface area generated by rotating the given curve about the y-axis. = 6t², y = 4t³, 0≤t≤1…

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Q: y = In[sin(x + y)]

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Q: Suppose that AABC is a right triangle with ZC = 90°.

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Q: f(x) = (5z – 3)(4: 6(2-0³) 3-20 f(9) = 3 ၁၂ နှ

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Q: Find the average rate of change of the function over the given intervals. f(x) = 12x³ +12; a) [5,7],…

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Q: Find an equation of the line tangent to the following curve at the given point. 2 5x 3' 6 y = T= 1…

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

A: The domain is the set of all possible input values  for a which function is defined.

Q: y'-(4/x)y=x^(5)*e^(x) how do I solve this differential equation?

A: The given differential equation is

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

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Q: These triangles are similar. solve for the indicated sides: X X +4 3 LO 5

A: Explaination of the answer is as follows

Q: The graph of a polynomial of degree 5 is shown. State the number of real zeros and the number of…

A: As we can see, the graph crosses the x-axis at x=-2So x=-2 has a multiplicity of 1The graph touches…

Q: 2. Show that the series converges by the Alternating Series Test (two conditions). Then find how…

A: The given series is

Q: Of all rectangles with a perimeter of 18, which one has the maximum area? (Give the dimensions.)…

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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: А = 1 1 1 3 4 -3 - 1 0 2 B || 8 -2 1 -3 1 0 - 4 1 1

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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: In the following exercises, use a change of variables to evaluate the definite integral. 2 294. ² t…

A: By changing the variables, to evaluate the following definite integral.

Q: Find T5 (2): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = Using the…

A: We have to find the Taylor polynomial of cosx of degree 5. Then using the Taylor Remainder Theorem,…

Q: Find the arclength of the curve x = -t³. 123 1²³, y = 2/1/1² t² with 2 ≤ t ≤7.

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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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