1. Answer the following questions for the quadratic function f (x)=x² -8x +8 . a. Calculate the vertex of f. b. Calculate the y-intercept of f. c. Evaluate f (7).

Q: Find the limit. Show all work. Vx +5 -3 1. lim- 2x? –x-3 COSX 2. lim X--1 3. lim x-/2 Cotx X4 X- 4…

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Q: Find the volume of the solid that results when the region bounded by y = Vā ,y = 0 and æ = 4 is…

A: Volume

Q: Solve the two items using Integration by parts. 1. [x' V9- x² dx 2. Te2* sin x dx

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Q: Directions: Prove the following statements. 1. If f(x) = (x² – 1)3 then f'(x) = 6x3 – 12x + 6x.

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Q: Solve the following differential equation y"+2y' +y=x-1 Select one: O a. YG.S= Ce¯+c,e¯2x+x-3 O b.…

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Q: If F(x) = f(g(x)), where f(2) = 5, f '(2) = 5, f (-2) = 1, g(-2) = 2, and g'(-2) = 5, find F '(-2).…

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Q: Find an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and (−1, 2, 3). Show all…

A: Here we have to obtain an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and…

Q: 9. 8. 13 3 f(æ)dæ = / f(x)dæ + f(x)de - f(x)dx, a 4 8. 4 what are the bounds of integration for the…

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Q: 2x – 6 X + 3 If f(x) = { x- 3 then the li X 5 X = 3 a. 5 b. 1 С. 2

A: Given for x = 3 , f(x) = 5

Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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Q: 2. Solve for x the equation sin1 3x - cos1 2x = 6

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Q: Find: d/dt (1/square root of 2t) A. square root of 2t/4t B. - 1/square root of 2t C. 1/2t square…

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Q: Find the Maclaurin series for the given function f(x) = e-6x

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Q: If y = 2u' and determine when x1. 2x-1

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

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Q: At how many point(s) does the helix with vector equation r(t) : (cos t, sin t, t) intersect the…

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Q: vergent, find its sum. (If the quantity diverges, enter DIVERGES.) 00 cos n° - Cos (n + 1)2 n = 1

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Q: Find the Taylor series generated by f at x = a. 1 f (x) a =3 4-x

A: Solve the following

Q: 6. 2y²e»² dx + 2xye»*dy = 0

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Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = -x + 7 6. g(x) = = y 81 6 2 bo 2.

A: We can find the area under the curves as below.

Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

A: Use area concept of integral

Q: 8. (x'-20) (x-3)

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Q: For what value(s) does the graph of y=3x5 + 10x4 have an infliction? A. 0 and -2 B. -8/3 only C.…

A: An inflection point is a point on the graph at which the second derivative is equal to zero or…

Q: Find 312 i-0

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Q: Find f' (x), if f (x) = 3Vx + 2Vx – 11 %3D

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

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Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: Is 34 = m, m being any real number, possible? Explain. [1C]

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Q: 5y² = 2x³ – 5y

A: Derivative with respect to x

Q: 19. A video store sells DVD movies and video games. Suppose 68 movies are sold at $25 each and 43…

A: Here given that 68 movies and 43 video games and the prices are $25 and $54 respectively.

Q: 1. Consider the function f(x) =-2(3x– 3)* + 1. a) State transformations. b) Use TWO of the following…

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Q: A physical education teacher found that 62% of the students exceeded the minimum standards. Which…

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Q: Find the Taylor polynomial of order 3 generated by x at a. 1 f(x) -, a = 0 x+6

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Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: * Find the 2nd degree Taylor polynomial for the function f (x)=- 1 centered at x = -2.

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Q: 8. Between 0°C and 30°C, the volume V (in cubic centimeters) of 1 kg of water at a temperature is…

A: density=massvolume For  density to become maximum, volume needs to be minimum. Given

Q: Demand Function: d(x)= 500-0.6x Supply Function: s(x)= 0.2x Find the Equilibrium quantity= Find…

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Q: For each problem, use implicit differentiation to find dy/dx in terms of x and y.

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Q: 486 on the interval [8, 20]. Find the absolute extrema for the function on the given interval.…

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Q: Determine the convergence or divergence of the series. n = 8 converges diverges

A: Given query is to find series converges or diverges.

Q: For the function y f(x) - la + 10: - df at x = 1. dx a. Find f'(1) = b. Find a formula for x =…

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Q: The vertical and horizontal asymptote for f(x) are X+4 a. x = -4, y = 0 b. no vertical asymptote, y…

A: Follow next step

Q: Evaluate the following integrals? .3 1)S x² e3* dx 2) S dx x²+25 dx 3) 6x – x2 4) | cos(In x) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: cesin x (sin x + cos x) dx e cos x

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Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

Q: 3. lim X→n/2

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Q: 21. Determine the value of k so that i = [- 5,k, 3] and i = [1,2, – 7] are orthogonal.

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Q: Let A(x) = | f(t)dt where f is the function given by the graph below. 4- 2 3 -2 -3 -4 A(2) = %3D…

A: Explanation of the answer is as follows

Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…