Find the extreme values of f subject to both constraints. f(x, y, z) = yz + xy;  xy =1;  y2 + z2 = 25

Q: Differentiate the function. Dy/dx y=1/(5x+8)^3

A: y=1(5x+8)3

Q: 1. Using the substitution 0 = 2 arctant, it is possible to transform any rational function of trig…

A: We have to-prove the equation,find formula for sin,find expression for ,compute the integral.

Q: 11. Find the exact area of the region bounded by the parametric curve x = cost, y = 2 sint; 0<t<2n.…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in  the…

A: Find the volume of the largest rectangular box in the first octant with three faces in  the…

Q: Computek(k+1) k=1 Hint: Use the fact that Ek-1(ak-ak-1)= anao (this is called telescoping) and…

A: The given series .The aim is to compute the sum of the series.

Q: Use the product rule to find the derivative of 10 (10x³ + 6x¹⁰) (5eª − 1) Use e^x for e. You do not…

A: The given function is

Q: Given f"(x) = 3x - 2 and f'(-3) = 5 and f(−3) = 6. Find f'(x) = and find f(1) =

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Q: Find the indefinite integral and check the result by differentiation. [(5x² + (2x152)dx (3x)² Step 1…

A: To find the indefinite integral and to check the result by differentiation.

Q: S x√3x + 1dx

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Q: 4. A water tank is shaped like an inverted cone with height 20 meters and base radius 5 meters. The…

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Q: -5-4-3-2 X 5 4 3 2 1 -2 -3 -4 -5- 1 2 List all the numbers x at which the function graphed above is…

A: since you have posted multiple question which are not interlinked so i have solved first question as…

Q: Find the limit of the transcendental function. lim ex cos(8x) X10

A: Here we will use the concept of limit, on putting x=0 in given function we will solve it

Q: At what point on the curve y = √3+ 2x is the tangent line perpendicular to the line 12x + 4y = 1? -…

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Q: ret/3 1 1 x cos(ln x)) dx

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Q: Consider the function f(x) = 5 - 8x² on the interval [-3, 7]. Find the average or mean slope of the…

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Q: A corporation has a continuous compounded bank account with 2.6% annual interest. The board of…

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Q: 1. Sketch the graph of an example of a function f that satisfies all of the given conditions. f(2)=4…

A: Given conditions of the graph,

Q: The size of a hole in a bursting balloon is modelled by the equation r = 54(4/3) where r is the mean…

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Q: Find d²y 2 dx 11 y=¹1√√x

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Q: nd [₁9(a) d g(x) dx = -10, evaluate the integral If g(1) = -4, g(5) = -4, and [₁²xg' xg'(x) dx.

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Q: Given h(x) Degree of h = 4 3x + 6x + 24x answer the following questions: The leading coefficient of…

A: The x intercept of a function is the point where the graph crosses the x axis.The yintercept of a…

Q: A graph of y= f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: A graph of is shown. In the same coordinate system, to sketch a graph of thederivative function…

Q: Let f (x) f'(x) = = sin−¹(x²) – tan−¹(6x + 1). Find the derivative of f. 6

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Q: Sketch a graph of f(x) = -(x-2)²-3 by using a sequence of transformations of a well-know make sure…

A: To sketch a graph of  by using a sequence of transformations of a well-known function.

Q: 2. Let P be the point (-3, 5, 4). (b) Find the distance from the point P to the yz-plane. Find the…

A: Let P be the point .(a) To find the distance from point P to the yz-plane.(b) To find the distance…

Q: The top of a 22 foot long ladder is sliding downward at 1.6 feet per second along a vertical wall.…

A: Length of the ladder =22 footThe ladder is sliding down the wall at a constant rate = 1.6 feet per…

Q: Find the amount that results from the given investment. $100 invested at 9% compounded quarterly…

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Q: Determine the derivative of the following function: ƒ(x) = ln(x² + 1)

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Q: 4) Solve the following linear equation for the indicated variable. Clearly show all your steps. What…

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Q: Suppose there are 9 different bottles of water and 9 different bottles of juice. (i) In how many…

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Q: 5. (a) State the formula for arc length (don't prove the theorem). (b) Find the exact arc length of…

A: The given function is

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

A: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

Q: Given y = f(u) and u = g(x), find dy dx y = tan u, u = 11x-4 = f'(g(x))g'(x) = dy -= f'(g(x))g'(x)…

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Q: 6. Sketch the graph of a function f with the following properties: • f is not continuous when x = 2…

A: We have to sketch the graph of a function with properties-f is not continuous when x = 2 but…

Q: Evaluate the Riemann sum for f(x) = x³ - 6x on the interval [0, 3] taking 6 subintervals and using…

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Q: 1. Consider the function f(x) = 6x³ - 10x² - 22x - 6 a. The y-intercept for the function is: b. The…

A: We have given a cubic equation and we have to find the -y- intercept,x- intercept,interval where…

Q: 100 100 100 t Σ ai = 6 and Σ b; = −4. Then compute Σ (2a; + 5b; – 3i + 1). i=1 i=1 i=1

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Q: Find dy (Do not simplify) clx d)y = (2x³- 3 + 5 √x - IT) (In (2sin (x)- 8 cos(x))) x 6) y = 3√√√x2 -…

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Q: 6. Consider the three points in the plane and their masses: P₁(5,-1) with m₁ = 4, P₂(-1,4) with m2 =…

A: We have to find the coordinates of the center of mass.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. S 23dx (x²-1) ²…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x² lim x→∞ 1-7x² Xx

A: Let,  F=

Q: Use any method to evaluate the integral. S- 22 dx (121x² + 1)²

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Q: Use the change-of-base formula and a calculator to evaluate the logarithm. Round your answer to…

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Q: 43.y=secx+cscx

A: Given data

Q: Sketch the region bounded by the curves y = 3 − x 2 and the line y = 2x, and find the area of the…

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Q: Find the Maclaurin series of Σ το sin(t) -dt.

A: To find the Maclaurin series of

Q: Find d²y dx y = 4x+9

A: Given, y=4x+9

Q: Solve the following problem and show your complete solution and explain your work. # 1. Find an…

A: Vertices (0,2) and (6,2)Asymptotes y=2x/3 and y=4- 2x/3Find the equation of hyperbola.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 9 y S- -dy 2 5у -у-2…

A: Integration

Q: et ƒ(x) = 3x² cos(4x). ='(x) = −12x² sin(4x) + 6x cos(4x) (2) = 17.245 "(2) = =

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