Express x = e e-31, y = 8e¹2t in the form y = f(x). (Use symbolic notation and fractions where needed.) y(x) =

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Q: Find a . b. a = (5, -5, 2), b =(3, 4, -1)

A: The dot product of a=a1, a2, a3 and b=b1, b2, b3 is: a·b=a1b1+ a2b2+ a3b3

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Q: 10) (a) Find the general indefinite integral F of (√x-2-4x) dx. Simplify your answer. (b) Find the…

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Q: Compute the derivative of the function y = 6 sin¹(x) at the point x = 1. (Use symbolic notation and…

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Q: 5 PM Fri May 12 learn-us-east-1-prod-fleetU 2) The position of a car moving forward in a straight…

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Q: 1 3 2- 1 ܐ im O

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Q: Find the length of the graph of f(x) - + 1 1≤ x ≤4

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Q: /(r) = = = 7²³ ) Approximate the change in the volume of a sphere when its radius changes from r =…

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Q: Use the functions given by f(x) = x + 4 O-43√x +4 O-43√x-4 ○ 43√x-4 43√x + 4 1 64 -x 4 and g(x) = x³…

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Q: Find the domain of function r(a) √22-32². Write your answer using interval notation in the box…

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Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:…

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A: We know that the speed formula =sqrt((dx/dt)^2+(dy/dt)^2)

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Q: Use the given zero to find all the zeros of the function. Function x³ + 13x² +59x+87 3,5±2i +3i, -5…

A: Given function is x3 + 13x2 + 59x +87 and it also given that -5 - 2i is a root .  Since -5 - 2i is a…

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Q: Find the area of the region. interior of r = 9+ sin(8)

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Q: Analyze the graph of the function. x³-27 x²-16 H(x)= (a) What is the domain of H(x)? OA. (x|x #3,…

A: As per our company guidelines we are supposed to solve first three subparts of a question so please…

Q: Find the derivative of the following function. f(x) = e⁹x + 7 In (5x − 2) 9x f'(x) = (Simplify your…

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Q: Find the Taylor series at x = 0 for the function by calculating three derivatives and using the…

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Q: A 10-ft-tall fence runs parallel to the wall of a house at a distance of 6 ft. Find the length of…

A: A 10-ft-tall fence runs parallel to the wall of a house at a distance of 6 ft. Find the length of…

Q: Evaluate the following limit. Enter the exact answer in fraction form, if necessary. To enter ∞ in…

A: let B=limx→∞(5x159x13+31x15)

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Q: D Use the Root Test to determine convergence or divergence (or state that the test is inconclusive)…

A: We have to find if the series converged or diverges.

Q: Use the graph to find the following limits and function value. a. lim f(x) x→1 b. lim f(x) x→1* c.…

A: The graph of the function is  To evaluate:  a limx→1-fxb limx→1+fxc limx→1fxd f1

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Q: Compute for y = [x² + 2] y = 3 1 x2 dy dx x³ + 2x + 1 (x - 1)² 3 X

A: Given that a function  and we find derivative of this function with respect to x. Here we use…

Q: Evaluate the integral. 1 1 x² X-2 2 x - 4x + 8 X-2 - 4x + 8 dx dx~ 0 (Type an integer or decimal…

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Q: Find the indefinite integral using the substitution x = 3 sin(0). (Remember to use absolute values…

A: The given integral is: ∫9-x2x dx

Q: Solve the inequality algebraically. 3x³>- 12x² List the intervals and sign in each interval.…

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Q: Given vector u =(−1, 1) and v = (−1, 1) and v = (–4, −2), determine the value of 5u - v in component…

A: u=<1,1> and v=<-4,-2> We have to find the value of 5u-v.

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Q: 6) lim X-0 x3 - 6x +8 X-2 A) -4 B) 4 piecewise function is given. Iso the mu C) 0 D) does not exist

A: limx→0x3-6x+8x-2

Q: Determine the following limits, using ∞o or -∞o when appropriate, or state that they do not exist.…

A: (a) Consider the provided expression, limx→-3+x+5xx+3 Apply the exponent rule,1ab=a-b. So,…

Q: ㅠ Let D be an ellipse rotated counterclockwise by radians, as pictured below. Before rotation, the 6…

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Q: Use the Maclaurin series sin æ = Σ(-1)"- n=0 1² st t Find the first three terms of the Maclaurin…

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Q: Two terms of a geometric sequence are given below  a6 = 972, a9 = 26244 Find the first five terms.

A: We know that the geometry series general formula a_n=a_1*r^(n-1)  Where a_1 first terms and r common…

Q: Evaluate the limit. lim f(x), f(x) = O-1 0 3 0-5 0-9 -x² - 4x4, -2, x‡ -1 x = -1

A: If limx→a-fx=limx→a+fx=k then  limx→afx=k

Q: y" 7. f(x, y, z) = 2x + 2y + z; x² + y² + z² = 9 f( X²

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A: The cost of producing x toys is given by x2+100x+2000The price of each toy is given by px=550-0.5x

Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

A: Consider the graph

Q: ind a vector a with representation given by the directed line segment AB.

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Q: Find the coefficient for the term afb5 from the expansion of: (3a - 2b)¹1 Answer:

A: We need to find the coefficient of a6b5 in the expansion of:(3a-2b)11