Find the area bounded by the curvey = x² + x +4, the x-axis, from x = 1 to x = 3. 16 14 12 10 y=x²+x+4

Q: Determine if the series O n=1 n cos (n) 3+n³ converges or diverges and choose the option that…

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: If x=c is a critical point of the function f(x) if f(c) exists and if either f'(c) =0 or f'(c) does…

Q: Sketch the region of integration and convert the polar integral to a Cartesian integral or sum of…

A: Please see the below picture for detailed solution.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: f(x) = 1 X-3

A: f(x)=1x-3if f'(x)>0, than f(x) is increasing if f(x)<0, than f(x) is decreasing d dx(xn)=nxn-1…

Q: Consider the graph below. Which of the following is the correct setup for the area of the shaded…

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Q: The function f(x) = - 0.625x^3 + 16.789x^2 - 102.722x + 658.154 approximates the number of…

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Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: Given: Limits include an arbitary real number, c.Find the limits limx→c+33(x-c)2 and limx→c-33(x-c)2

Q: Solve yy'= -(x+2),Y(0)=\

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Q: Find the critical point of the function f(x, y) = −8+2x+4x² + 5y-y² This critical point is a:…

A: Given f( x, y ) = -8 + 2x + 4x2 + 5y - y2

Q: 1. Find the limit limä→∞ (1 + 3 X 5x

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Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: Find the general solution to the non-homogeneous differential equation. y" - 4y' + 5y = 7e-x y(x) =

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Q: = 1/₂ F² A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and…

A: We have to find the integral.

Q: a) lim x-0 9+x-3 x

A: The solution is shown below-

Q: Suppose the demand for a certain brand of a product is given by ​D(p)=−p^2 / 416+450​, where p is…

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Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

Q: 2. Optimization problem The average cost per unit when producing x units of a commodity is given by…

A: Solved below

Q: Find the general solution to the given differential equation. (Remember the constant of…

A: To find general solution of differential equation As per our guidelines we are supposed to answer?️…

Q: 6. What principal invested at 13% compounded continuously for 6 years will yield $9000? Round the…

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Q: Estimating the Amount of Paint Required A coat of paint of thickness 0.07 cm is to be applied…

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Q: find a reduction formula for the integral|x" cos x dx.

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Q: Complete the parametric equations of the line through the point (2,-6,-2) and perpendicular to the…

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Q: Evaluate the integral. 2 √√Z T ||||** SS (² cos ²0+z²)r de dr dz 000 2 √Z T S SS (² cos ²0 +2²)r de…

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Q: Find the derivative of the function. -7x³ - 6 6x² +7 f(x)=

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 4 sin…

A: By using the double integration to find the area of the plane region  enclosed by the curves. y=sin…

Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: To find where the function is increasing or decreasing.

Q: - The function ƒ(x) = 2x³ − 33x² + 144x – 2 has two critical numbers. The smaller one is x = and the…

A: Please see the below picture for detailed solution.

Q: Differentiate the function. f'(x) = f(x) = 250

A: f(x) = 250 We need to find f'(x)

Q: Let C(x) represent the cost of producing x units of a particular commodity where C(10)=1000 and…

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Q: Let f(x) = x² - 5x - 6. Find the open intervals on which f is concave up (down). Then determine the…

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Q: Suppose a product's profit function is given by π(q) 3q² + 800q, where (q) is in dollars and q is…

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Q: Consider the curve 1x² - - 2xy 1y³4.25. (a) Find an expression for y'. y' = (b) P(-1.5, 1) is on…

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Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = t² + 3t.…

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Q: Find the unique solution to the differential equation that satisfies the stated conditio dy In(x) dx…

A: given:differential equation dydx=lnxxy,  y1=6

Q: The average rate of change of f(x) = X a. 2 b. 0.5 over the interval 1 ≤ x ≤ 2 is c. -0.5 d. -1

A: we will find the required.

Q: Find the points on the cone ² = x² + y² that are closest to the point (5,2,0)

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: A function y=f(x) is said to be increasing in the interval (a,b) if for every x∈(a,b), f'(x)>0.…

Q: Describe the given region in polar coordinates.

A: Please see the below picture for detailed solution.

Q: Find a plane containing the point (-5,6,5) and the line Calculator Check Answer x (t) y(t) z(t) = =…

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Q: Solve using the elimination method. 0.2x 0.5y = 1.1 0.5x 0.2y = 1.7 (Hint: Since each coefficient…

A: 0.2x-0.5y=-1.1.....(1)0.5x-0.2y=-1.7..........(2)

Q: 30. Given g(x) = 4x² + 1, use the difference quotient to find the instantaneous rate of change when…

A: Given function:- gx=4x2+1

Q: 2. Determine whether the series is convergent or divergent. If it is convergent, find its sum. ܐ 5…

A: The Series ∑n=0∞arn is called geometric series and the geometric series a is the first term and r is…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: The concentration of the antibiotic in the bloodstream is modeled by the function C(t) = 6(e−0.4t −…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: Determine whether Rolles theorem can be applied to the function. f(x)=(x-5)(x-6)(x-7) on the closed…

A: we have to slove above question f(x)=(x-5)(x-6)(x-7) on the closed interval [5,7]. find all numbers…

Q: Find the critical point of the function f(x, y) = 4+ 3x + 2x² − 4y − 2y² This critical point is a:…

A: Need to find out the critical point of the given function.

Q: Find the derivate of the function F(x) = x²(x²-8) a) C 2 6b) f(x) = (5x²³²-7) (6x + 1) F'(x) = c) 5…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 3. Evaluate the limit for the graph: lim f(x). x+1* y 4 2 01 -2 2 48 x

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