2 Find the area between the graph of y = 5 – 5x³ and x-axis and − 1 ≤ x ≤ 8 using properties of definite integrals.

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Q: 1 x 69. g(x) = ₁ ₁³ + 14 dt 3

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Q: Determine the values of constants a, b, c, and d so that f(x) = ax³ + bx² + Determine the values of…

A: Given,            fx=ax3+bx2+cx+d has a local maximum at the point 0,0 and a local minimum…

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Q: Find the derivative of the function. y' = an−¹(x - √√₁+x²) 2 1 y = 5 tan

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Q: 23. lim 848 5√√x+3 1 - 17x²

A: Solve limit

Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: At time t, the position of a body moving along the s-axis is s = t³ - 9t² +24t m. a. Find the body's…

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Q: Find the derivative of the function g(x) = g'(x)= = e² 4 - 2x

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Q: Use the information to determine the limits. (If the limit is infinite, enter 'co' or '-co', as…

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Q: If a principle of $4000 is invested at an interest rate of 6%, how many years will it be until the…

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

Q: Differentiate the function. f'(x) = f(x) = x7³ − x + 8

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Q: Write a formula for the nth term of the following geometric sequence. Then use the formula for an to…

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Q: 14. √9-x² x2 S dx

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Q: If ["F(x) 1.2 f(x) dx = 7.2 and nd ["fix) dx = 5.6, find [° F(x) dx. X

A: we know that ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where c is betwwen a and  bgiven  ∫17f(x)dx=7.2 and…

Q: Topic: Time Rates: Inverse trigonometric functions A balloon leaves the ground 500 feet away from…

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Q: Find the equation of the line through the point (-5, 4) and perpendicular to the line y = 2-5.…

A: In this question, we want to find a equation of the line perpendicular to the given line passing…

Q: Question 1: A radioactive element has a half-life of 30 years. If you begin with 7000 grams of the…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: sin(2x) x y = if x = л, dx = 0.25 find the differential. Round your answer to three decimal places.

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Q: 1 1 1 은 관 + dt

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Q: 5 If ["f(x) dx = 8.1 and ["f(x) dx = 3.7, find rox) f(x) dx.

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Q: Write Sk 1.13+2 14+3•15+...+ Write SK+1- (Type your answer in factored form.) 1.13+2+14+3•15++=…

A: To evaluate:  ------------------------------------------------------------------------------- Basic…

Q: 19. lim x²-5x-24 x-5 x²-9

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Q: If (2,-5) is a point on the graph of f(x), which of the following points MUST be on the graph of…

A: Given that point (2,-5) is a point on the graph of f(x).

Q: The surface of a machine part is the region between the graphs of y₁=1x and y₂ = 0.100x² +2.500 as…

A: Given that , y1=x , y2=0.100x2+2.500 Find the area of the surface of machine port.

Q: The measurements of the base and altitude of a triangle are found to be 46 and 34 centimeters. The…

A: Given information altitude ( A ) = 34 cm Base ( B ) = 46 cm let Area = A

Q: Solve the equation: 3*²-5x x = 3 x = 5 and x = -5 O x = -5 x = 3 and x = -5 || 27.

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Q: Consider each function to be in the form y = kx, and identify k or p as requested. Answer with the…

A: Given function y = k.xpy = 1πx

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: er the equation of the parabola graphed below, using the vertex form y = a (x-h)²+k. y = (-1,0)…

A: To solve the following problem using graph

Q: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) =…

A: given  rate  r(t)=120e-0.02t∫eatdt=eata+c

Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: Find the values of sin(0), cos(0), and tan(0) at the given points on the unit circles in the figure…

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Q: EC: Find the derivative of g(x) (x) = = 0 cos(t²) dt cos(1¹) di

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Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

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Q: X √4- 4+3x² -dx

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Q: 3) lim X^ X-O' B) i A) O де D) ∞ a(3) = 3₂ E) nove eriste

A: Given query is to find indicated limit.

Q: 5) Find the divergence of (√x² + + z ²) kî + yî + zk)

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Q: Find that interval) Find 4√√x +3 Sv Find a number c in [1,4] where the integrand achieves its…

A: We have to solve that,…

Q: Write Sk k: 4+8+12+...+ -0-0 Do not simplify.) Write SK+1. k+1:4+8+12+...+4(k+ 1) = Simplify your…

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Q: (c) At what points is the height 40 m? (Round your answers to two decimal places.) (x, y) = -52.825…

A: The given equation of the arch:y=211.49-20.96 cosh0.03291765x

Q: Find f(a), f(a+h), and the difference quotient f(a+h)-f(a), where h * 0. h f(x) = 4 - 2x + 7x² f(a)…

A: Let's find all given function value.

Q: Topic: Maxima-minima/optimization problems: Inverse trigonometric Functions For example, suppose we…

A: Minimum value= -pi/2  Maximum value = pi/2  For detail...go through the solution

Q: The differential equation below models the temperature of a 87°C cup of coffee in a 23°C room, where…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Graph the integrand, and use area to evaluate the definite integral The value of the definite…

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Q: Does the series converge conditionally ot absolutely

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Q: You are attempting to evaluate the integral What trig substitution would you use to simplify this…

A: Given the integral is ∫9x2-9x dx

Q: Solve the following initial valuc problem using the method of Laplace transforms y" - 4y + 5y = 8c³;…

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