a²+ax+b The curve Y has a local minimum at (3, 8). Determine the values of a and b. x-1

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: Here ,              We have given a vector valued function now we have to determine the intervals on…

Q: The following figure shows the graphs of y = f(x) and y = g(x), together with the indicated %3D %3D…

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Q: (-2 if XS-1 S(x) = {x² -3x+8 if if -1<x<2 x22

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Q: 3. y = Væ – 1, æ = 5 , y = 0 , revolved at y axis

A: To solve the following problem

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A: Using she'll method, volume is evaluated.

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Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: Consider the points A(2, –3, 4), B(4, –5, 1), C(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: In(1+x) ferentiate f to determine the sum of the series n= +

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given : r(t) =36-t2i + t2j-2tk   To Find : Domain

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Q: Find the area of the region enclosed by the rose r = 2 cos 30. NOTE: Enter the exact answer. A ||

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Q: Find the values of constants a and b that make f continuous on (-o0, +o0) where 2x +1 if a 5 f(x) =…

A: Use definition of continuous function and find the value of a and b

Q: Find the volume of the solid that results when the region enclosed by the curves x = 1 – y² and æ =…

A: Let's find.

Q: Consider the following optimization problem. Maximize P = xyz with x + y = 36 and y + z = 36, and x,…

A: We have to find P(y), P'(y) and maximize P.

Q: If R is the region bounded by y = x* – 1 and y = -x² – 1, find the volume V(S) of the solid S…

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Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) %3D х3 — уз,…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The integral represents the volume of a solid of revolution. 27 x³ dx (a) Identify the plane region…

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Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A: Given:      fx=7sinx2 interval 0,π4 Volume of solid using cylindrical shell method is…

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: The domain of y = arcsinx is: -13x<1 all reals O-I to !

A: I am attaching image so that you understand each and every step.

Q: (y + 1)dx + (4x - y)dy 0

A: Explanation of the answer is as follows

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: The following figure shows the graphs of y = f(x) and y = g(x), together with the indicated areas. C…

A: to

Q: Find the gradient of the function at the given point. g(x, y) = 13xeY/x, (5,0) Vg(5, 0) =

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Find the intersection points of the pair of ellipses. S4x2 + y2 = 4 (4x² + 9y2 = 36 %3D ([ (х, у) 3…

A: We know that standerd form of an ellipse is :- (x-h)2/a2  + (y-k)2/b2 = 1     Here i attached the…

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Q: Determine which value best approximates the surface area of z = f(x, y) over the region R. (Make…

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Q: a) Find the intervals where the function f(x) is increasing or decreasing b) Find the intervals…

A: Follow the procedure given below.

Q: A tin can has a base diameter of 10 cm and a height of 10 cm. The can is initially full, but a hole…

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Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

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Q: Use the comparison test to test the series n2- 1 n =1 クタ

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Q: f (x) = x² – 2x ; a = 1 f (x) = |x| ; a = 0 f (x) = ; a = 0 3 x+1 f (x) = ; a = 3

A: f(x) =x2-2x  ,From graphContinuous and differentiable at a=1

Q: Differentiate Derivative of Derivative Differentiation Outer of Inner Function Function 1. y =…

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Q: Given that f(x, y) = 8x-2x² - y² +8y with the constraint g(x,y): 2x+y=5. Determine the optimum value…

A: Solution is given below:

Q: Which of the following p-series is convergent: 1 Σ 00 n=1 5 n=1 n n=1 5 1 n=1 15 n

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Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: A product is introduced to the market. The weekly profit in dollars of that product decays…

Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

A: We can solve this as follows:

Q: The following figure shows the graphs of y - f(x) and y = g(x). together with the indicated areas.…

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Q: Let f be a continuous function. Show that 2022 f(1/a) dx f(x) dz. %3D 1/2022

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Q: F0 (-1)" Ln=1 By the 5n+1 series test:

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Q: Find the curvature K of the plane curve at the given value of the parameter. = ti +tj, t = 3 36 r(t)…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 + 3y + z = 5 Find the normal vector, n,,…

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