Find a power series representation for the function and determine the radius of convergence. f(x)=D 11-7x

Q: What is the slope of the tangent to the curve y=arctan 4x at x= 1/4 A. -2 B. 0 C. 1/2 D. 2…

A: To find the slope of tangent to the given curve.

Q: Give the generator, the directrix, and the rulings of the cylinder x = lnz. Draw a sketch of the…

A: We need to give generator, the directrix, and the rulings of the cylinder x = lnz.

Q: Find y if y= 3(x³ – 7x+2)5 +4x -2.

A: Topic = Derivative

Q: Prove the following by Mathematical Induction 1. 1/1(2) + 1/2(3) + 1/3(4) +...

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Q: de 1+sin e+ cose CO

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Q: Use the formula K(t) ||r(t) × r"(t)|| to find x(t). r(t) = 2 cos(4t)i + 2 sin(4t)j + 9tk K(t) =|

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Q: | 3t³ (t² + 4)5dt

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Q: 3. Let the statements A, B be A: (not p) and q, B: (not p) or (not q). If p 0 and q = 1, then !! %3D…

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Q: E. Find the value of D, E, and F of the following circle that passes through (-1, 4)(3,2) and (5,2)

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Q: If f(x)=-(x² – 4), find (a) The x-intercept and the y-intercept (b) The interval where the function…

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Q: The region bounded by the curve y= x² and the line y=3x is revolved about c) the line x=-3 b) y-axis…

A: This is a problem related to volume calculation by solid revolution. Based on the general formula…

Q: Rates of Change: Oscillating Spring At Answer the following question, and give a written…

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Q: The point (4, k) lies on the ellipse 32 y? = 1. 18 Which of the following could be a value for k? 0…

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Q: —x2 — 4х + 18 (Зх+ 4) (x? + 9)"*

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Q: 30. The number of floats in the last Panagbenga Festival is about 50. This year, it is expected that…

A: Use permutations method nPr=n!/(n-r)!

Q: 9. Suppose that the demand equation for a monopolist is p = 100 – 0.01.x and the cost function is…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 13. Given the points A(3,5) and B(- 3, - 7), find a. the vector equation of the line. b. the…

A: Here, the given points are A(3,5) & B(-3,-7)

Q: Consider the function f(t) : 8 sec-(t) – 10t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Topic = Anti derivative

Q: 5. Evaluate the expression without using a calculator. Sh (a) sin (쓰) (b) cot(-210°) (c) csc(cos-1…

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Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: Demand for the latest best-seller at OHaganBooks.com, A River Burns through It, is given by q = -p2…

A: This question can be solved using the concept of absolute maximum.

Q: 2. Write the given (total) area as an integral. a. The area above the x- axis and below y = 4-x2 NI…

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Q: 1 7. (x dy – y dx) = 0 x² + y?

A: We are given a differential equation  1/(x2+y2) ×(xdy - ydx ) =0 We have to determine whether it is…

Q: Find the volume of the solid that results when the region enclosed by the given curves y = e-2, y =…

A: The given curves are; y=e-2x, y=0, x=0 and x=1 So, the bounded region is as shown below. Apply the…

Q: -2V-6 6. The gradient of a curve is given by = 3). find the equation of the curve. Given that the…

A: Equation

Q: (y* - 2xy)dx + 3x?dy = 0; when x = 2, y = 1

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Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = x2 - 7x + 6 g(x) -x2 + 5x + 6 y 10…

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Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: To find the equation of curve

Q: x + 4 dx x² + 2x + 5

A: ∫x+4x2+2x+5dxx+1 is a scalable factor of x2+2x+5, so divide x+4 by x+1=∫x+1x2+2x+5dx+∫3x2+2x+5dx

Q: If an alternating series is not convergent then it is divergent. Select one: O True O False

A: We can find the answer as below.

Q: Find the 44th derivative of the function f(x) cos(2). = The answer is function f 144) (æ) = cos (x)…

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Q: 2. Let R(t) = } sin 4t î – bcos“(21) j + 2t k. E

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Q: What are the slopes of the asymptotes for the hyperbola whose equation is 4x2-9y? = 36? %3D

A: Here, the given equation of the hyperbola is: 4x2-9y2=36 In standard from it can be written as:…

Q: Using a trigonometric substitution, the integral dz becomes: 2+25 (a) 25 (tan 0) (sec 0) de (b) 5 /…

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Q: Evaluate the integral mx sin nx dx

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Q: e-(x²+y³)(x dx + y dy) = 0

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Q: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

A: 1) To find the largest interval on which the function f(x)=x+3 is conitnous.

Q: S- |-3x cos 4x dx 3 A)- cos 42 -x sin 4x +C 16 B) cos 4x --x sin 3x + C 16 3 cos 4x - 16 cos 4x - 3x…

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Q: Sketch the figure or analysis. Shade the needed region and draw representative vertical or…

A: Follow the procedure given below.

Q: emx cos nx dx

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Q: Find the indefinite integral and check the result by differentiation. (e5+ sec e) de

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Q: This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A…

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Q: What is the equation of the circle with centre (,0) and radius 2? (2a- 1)2 + y? = 2 4. (2x-1)2 + y?…

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Q: Describe the graph of the equation. r = 19 sin 2t i + 19 cos 2t j O It is a circle of radius 19 in…

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Q: 8 sin z 6 sin z + 4 cos a Let f(x) = Then f (2) = The equation of the tangent line to y = f(x) at a…

A: Given: f(x)=8sin x6 sin x+4 cos x f'(x)=(6sin x+4cosx)d(8sin x)dx-(8sin x)d(6sin x+4cosx)dx(6sin…

Q: Finding the Area Bounded by Two Graphs Sketch the region bounded by the graphs of the functions. See…

A: This is a problem related to area of the intersected region by given curves. Based on the general…

Q: 12. Given f (x) = x³ – 12x + 1 (a) Find the intervals on which f(x) is increasing or decreasing. (b)…

A: I have appended the formula used in the solution part.

Q: Sketch the graph of the following equation 2x + 6y + 3z = 12

A: To sketch the graph of given equation

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) -

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Q: SIXE-A Consider the graph shown to the right 4. lim f(x) X-axis 5. Evaluate lim f(x) X+3" 6. lim…

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