Evaluate the indefinite integral as a power series. fin(1+x²) dx

Q: f(x) = −x+10 g(x) = x² − x − 11

A: Given that the function

Q: Which of the following represents the limit definition of the definite 16 integral 26 4x5 dx using a…

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Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

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Q: At which of the value(s) of x below does f(x) = ²³² +5x² + 25x + 1 have a horizontal tangent line? O…

A: Given that, the function is .We need to find the value of x for which the given function has a…

Q: Sketch the graph of the quadratic function. f(x) = x² — 20x – 800 - -

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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: The total revenue for a product can be calculated as the area under the demand curve. Suppose that…

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Q: Consider the following graph of f (x). Which of the following are inflection points of f (x)? -3 O…

A: We have to find the coordinates of the inflection points from the given graph of function.Let's…

Q: Consider the functions f(x) = 6 arcsin (6x) g(r)= 12arctan (a) Find the derivatives of f(x) and…

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Q: Consider the indefinite integral ax + b + where Then the integrand decomposes into the form C d a =…

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Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'(x)= 0.03x2-0.08x+189

Q: Given y = f(u) and u = g(x), find - (3) ² y=9u-5, u= dy dx = f'(g(x))g'(x).

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Q: An equation of the ellipse is

A: Given that the graph of the ellipsewe have to find equation of the ellipse

Q: Let sin A = -1/sqrt10 with A in QIII and tanB = 3/4 with B in QI. Answer exactly. Find tan (A+B) and…

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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: Let Z₁ = 6(cos(72) 7π -54 Z1Z2 = Z1 = Z2 + i sin (77)) and Z₂ = X 9(cos(55) + i sin (57)). Find Z₁Z2…

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Q: The point(s) is/are (Type an ordered pair. Use a comma to separate answers as neeeded.)

A: Given that the graph with tangent line parallel to y=3x+1 we have to find the point is/are?

Q: 56. The length of required to enclose a rectangular field is 3000 meters. What are the dimensions of…

A: Let the length of the rectangular field=x mLet the width of the rectangular field=y mThe figure of…

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

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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: The velocity function v(f) (in meters per second) is given for a particle moving along a line.…

A: We have to find the displacement and distance travelled by a particle in the given interval.We will…

Q: sin x lim X→0 xX tan x m. n. lim x→0 X

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Q: Find the area of the region bounded by the graph of f(X) = Sin X and the X axis on the interval [-2…

A: Given:

Q: Suppose parametric equations for the line segment between (4, 2) and (4, - 2) have the form: [ x(t)…

A: The line segment between the points (4, 2) and (4, -2) has parametric equations,It is also given…

Q: Let f(x) be a continuous function for which we know f(2)=3, f(4) = 5, f'(2) = 7, and f'(4) = 19.…

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Q: Find the equation for the line tangent to the parametric curve: at the points where t = 4 and t =…

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Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = t³i + 3t²j, t…

A: The given equation of curve

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cos³…

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Q: he table gives the values of a function obtained from an experiment. Use them to estimate f(x) dx…

A: Consider the given table in the question.Given that n = 3△x=b-an"…

Q: Find the radius of conv- 00 n! n 1.3.5..... (2n

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Q: 15. A hot-air balloon is rising straight up at 5 ft/sec. An observation area is located 80 feet from…

A: Hsnsnsn

Q: 2. Evaluate the integrals. a. b. C. L (6x - e²) dx [²₁12 +2 (2 + 2y)² dy 7T/4 3 3 sec Ꮎ tan Ꮎ ᏧᎾ

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Q: Find the slope of the line tangent to the polar curve at the given point. 7x (-3- r= 6 sin 0; Select…

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

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Q: Find ∫∫R  −3x+5y/(x+6y) dA where R is the parallelogram enclosed by the lines −3x+5y=0, −3x+5y=3,…

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Q: 4. Using Geogebra, draw the parametric curve, x = sin³t+cos³t; y = sin² t - cos²t,0 ≤t≤ 2n-

A: The given curve is,The given interval is,

Q: L³₂x³dx -2 2 1 x+0.5 dx

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Q: Find and simplify the difference quotient f(x) = 8 f(x+h)-f(x) h h#0 for the given function.

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Q: Find the Derivative and the Line Tangent to a Curve at a Point. 2 (-2x - 3)² Given that R(x) R'(x)…

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Q: The function C(t)=C0(1+r)t models the rise in the cost of a product that has a cost of C0 today,…

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Q: Let f(x) = 3x - 6 and g(x)=x+3. Find each composite function and describe the domain of the…

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Q: 12T 4. Evaluate in Cylindrical Coordinates D bounded by z= x² + y² and the plane z = 4 ff zdxdydz

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Q: Let p(x) be a polynomial of degree 3. Its derivatives, around the point x = -5, are as follows: What…

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Q: 9. In the following exercise: i. Identify the function's local extreme values in the given domain,…

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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: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

A: Given,

Q: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

A: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

Q: 3/4 Find the cost function if the marginal cost function is given by C'(x) = x C(x) = +5 and 16…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. M8 Σ…

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Q: 224. Suppose that a particle moves along a straight line with velocity defined by v (t) = t² – 3t –…

A: According to our guidelines we are supposed to answer only the first question if you want any…