Find the linearization L(x) of the function at a. f(x) = cos x, a = 3π/2 L(x) =

Q: Let y be defined implicitly by the equation In (4y) = 3xy. Use implicit differentiation to find the…

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Q: Differentiate. d y = log 4 (xº + x) - log4 (x8 + x) = □ dx

A: To differentiate the following function.

Q: 11. A conical water tank with a vertex angle of 60° is being filled with water at a constant rate of…

A: Let r be the radius of the water surface and h be the height of the water inside the cone at any…

Q: 2t - e -2t Let h(t) Find the horizontal asymptote(s) of h(t) if they exist. If h(t) has no…

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Q: Find the eigenvalues of the matrix -40 -18 2 -8 -18 -14 -8 -18 -14, Enter the eigenvalues as a list…

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Q: Evaluate the following integral 8 ["* e* dx е 0

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Q: Let F(x) = f(xf (x²)). Suppose that ƒ(4) = 6, ƒ'(4) = 1, and ƒ'(12) = 5. Find F'(2).

A: Given, .Given,  f(4)=6, f'(4)=1 and f'(12)=5.

Q: Simplify the rational expression. y³ - 27 -y² + 9y - 18

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Q: Differentiate the function. y = log (e-* cos(TX))

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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Q: Determine the equation of the tangent to the graph of y-²-4-√x at the point (4,8). a) y=-7x+36 b)…

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Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

A: Given that a model used for the yield Y of an agricultural crop as a function of the nitrogen level…

Q: Let f(x) = x² and g(x) = (x − 1)² + 4. There is one line with positive slope that is tangent to both…

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Q: 3. ftan5 4x sec³ 4xdx.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Match each trigonometric function with its derivative. Enter the correct letter in the box beside…

A: Given, (A)

Q: For the function f(x)=simplify the difference quotient: b) [(x+h)-700 What is the slope of the…

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Q: Graphs of the velocity functions of two particles are shown, where t is measured in seconds. When is…

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Q: Find the solution to the boundary value problem: dy - 6- dt The solution is d²y dt² - +13y = 0, y(0)…

A: we are given the differential equation and we need to find out the solution.

Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

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Q: The graph of y = f(x) is shown below. -7-6-5-4-3- T .F. 5 4 3 2 1 2 3 4 4 H 3 4 5 6 7

A: From the given graphParent function f(x)=y=x2

Q: a) Find formula for f(x) if f(x) = 5x-1

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Q: 1. Change the equation x² + y² + 6x - 16 = 0 to standard form and determine the coordinates of the…

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Q: Find the logarithm using the change of base formula. log 590 log 590 = (Round to four decimal places…

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Q: = Let F be the vector field F(x, y, z) = xi+yj +4zk √²+2 beneath the plane = = 3, oriented using a…

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Q: Find the angle of intersection between the curves: y² = 4x and 2x²=12-5y at (1,2) to three…

A: Angle between the two curves is given by

Q: Find the logarithm using the change of base formula. log 717 log717= (Round to four decimal places…

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Q: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…

A: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…

Q: Find the exact directional derivative of the function √y z at the point (1,9, 9) in the direction…

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Q: 2. For what values of n does this integral converge or diverge? Show all evidentiary work for each…

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Q: Suppose that a colony of Jeevesium beetles grows exponentially with doubling time 7 years. How many…

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Q: Find the length of the curve x = 6y from y = -5 to y = 5. Write the exact answer.

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Q: 2. Does the following function satisfy the preconditions of the Mean Value Theorem on the given…

A: Mean value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: Differentiate. f(x)= x³ In 7x 3 f'(x) =

A: Product Formula for differentiation is given as follows

Q: Solve the differential equation. (t−8) s' +7(t−8)5s=t+8, t> 8

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Q: Let F = (z, xy, x² + y²). Compute the work done by the force when moving a particle located at the…

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Q: Let f(x) = In(x). State if the following statement is true or false (a) The graph of f(x) has a…

A: According to bartleby guidelines we are supposed to do only one question.  If you want more to be…

Q: Find dy dy dx by implicit differentiation. tan(x - y) = = y 7+x²

A: Here to find implicit differentiation , we must differentiate both sides of the simplified form of…

Q: If then the domain D of the function f is given by the set Select one: ○ {(x,y)|y² > x, ○ {(x,y) y²…

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Q: 4x(4-x2)1/2  Find the antiderivative

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Q: A regression was run to determine if there is a relationship between hours of TV watched per day (x)…

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Q: (Multiple Choice Question) If sec a = -3 = tan ß and a, ß € [T, 2π], then sin(a + 3) is equal to:…

A: Given that and

Q: Determine the vertex of the parabola whose graph is given below. MMM 6 5 4 S 2 -7-6-5-4-3-2-1, 1 2 3…

A: The graph of the parabola is To determine: The vertex of the parabola.

Q: Given function f (x) = x3 − 12x + 2, (a) find the intervals of increasing or decreasing (b) find…

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Q: 2. a. b. The distance travelled by an object is given by the equation: d(t) = 20t 1+t2 t20. What is…

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Q: Evaluate the definite integral. re4 dx 1 x√In x

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Q: Ihd an equation of the line tangent to the curve y = An equation of the tangent line is 5x 2 x +4 at…

A: Here we will solve it on finding the slope at x=4 after that we will use the formula of equation of…

Q: Application of De A tank contains 1,200 liters of fresh water. Brine containing 0.2 kg/liter of salt…

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Q: Compute the derivative of the following function. f(x) = 5xe-5x f'(x) =

A: we need to find out the derivative of the given function.

Q: 7. Given the graph: (a) Given P(x) = f(x)g(x), find P′(2) f(x) (b) Given Q(x): find Q'(2) g(x)' =…

A: Given the graph:

Q: In 2004, an art collector paid $155,328,000 for a particular painting. The same painting sold for…

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