Evaluate and simplify y'. 5x²-9x 2 3x+4 y=- y'=0

Q: Suppose z = x² sin y, a = 48² t², y= 8st. A. Use the chain rule to find and all x, y, s and t in…

A: z=x2-t2 ,y=8st

Q: Let f(z) = 10 +4-15e*. Find the equation of the tangent line to the graph of f(x) at the point (0,…

A: The function is The point on the graph of  at which the tangent line equation needs to be determined…

Q: Evaluate this function at x=6. Express your answer as an integer or simplified fraction. If the…

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Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

A: The given function is

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

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Q: The arc length function for a curvey = f(x), where f is an increasing function, is s(x) = √√5t+10…

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Q: If f(x, y, z) = x²y³ — 4x, find the directional derivative at (1, 1) (3,-4). in the direction given…

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Q: 4. Find the following limits. If the li -∞0, write that. (a) e³x-1 lim x→0 5x

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

Q: f(x)=x² - 4x-7; [-1,3] The absolute maximum value is at x=0 (Use a comma to separate answers as…

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Q: Find the length of the indicated portion of the curve by first finding the arc length parameter…

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Q: Solve the initial value problem. dr/dt=-5ti+5tj+9tk. Initial condition r(0)=-4i+5k

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Q: / 2 - 100% + A A particle moves according to the equation of motion s = t5 - 10t³ + 18t, where s…

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Q: Let G=7f-g, where the graphs of f and g are shown in the figure to the right. Find the following…

A: G=7f-g

Q: Sunset Lake is stocked with 2600 rainbow trout and after 1 year the population has grown to 7000.…

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Q: A tank contains 1140 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

A: The tank has 1140 L of pure water.Solution has 0.03 kg of sugar per liter enters the tank at 3 L/min

Q: Find a particular solution Y of the differential equation 8y" + 2y' + 3y = sin²(x). using the Method…

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Q: Match each linear equation with its graph P K B R * G I Equation < Y 32 2x+1 vy=x 3 y = 5x 3 y=-2…

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Q: In 1991, the moose population in a park was measured to be 3710. By 1998, the population was…

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Q: Write an equation for a line parallel to y - y = 2x 3 and passing through the point (2,0)

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Q: 3. For the function g whose graph is given, state the following. (a) lim g(x) (b) lim+g(x) = x48 (c)…

A: Note:-As per your demand we solve question 3 for you The condition of existence of limit at

Q: Assume that the x- and y-axes are rotated through angle 0 about the origin to form the x'- and…

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Q: The limit below represents the derivative of a function f(x) at a point zo. Give the equation for…

A: The  limit below represents the derivative of a function  at a point .To give the equation for  and…

Q: F'(x) = f(x) = 4x5-35x² + 40x Compare the graphs of f and f' and use them to explain why your answer…

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Q: Given F(r, s, t) = -r (3s5 + 6t5), compute: Frst

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Q: Write the augmented matrix of the given system of equations. 0.05x -0.04y 0.17x+0.40y = 0.04 0.30

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Q: Consider the following function. x ≤ 1 (3x + 2, 16-x², x > 1 (a) Find the critical numbers of f.…

A: The given function

Q: Find the linear approximation of the following function at the given point a. f(x) = sinx, a - ㅠ ▬ 2

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Q: Find the local linear approximation of f(x) NOTE: Give your answer in terms of x and not Ax. 1 √1+x…

A: we need to find out the linear approximation of the given function at the given point."Note that as…

Q: Differentiate the function. f(x) = log,(xe*) F'(x) =

A: Consider the function Formulas

Q: Find the derivative of the function. g(x) = sec¯¹(8e*) g'(x) = X

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Q: Find the angle between u and v in radians. Round to the nearest hundredth of a radian.u=-4i-7j,…

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Q: Evaluate the following limit. (7x² - y²) lim (x,y)→(6, -6)

A: Let,

Q: The population of Vero Beach can be modeled by the function P = 17234e0.01921t where t is the number…

A: where t is the number of years since 2020

Q: Suppose that Σ an = -3 and n=] ∞ A. Σ(-6an + −8bn) n=1 = B. (-6an +-8bn) n=2 = ∞ n=1 bn = -5 and a1…

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Q: Using the given graph of the function f, find the following. (a) the intercepts, if any (b) its…

A: we are given the graph and we need to find out the x-intercepts, y-intercepts, domain, range, and…

Q: Find the derivative of the function. f(t)=√3+ tan(t)

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Q: 2. Complete the Square to re-write the quadratic equation in vertex form and graph the function:…

A: The given quadratic equation is The vertex for of a quadratic equation with the vertex  is

Q: Find equations of the tangent plane and normal line to the surface z-4 = ze cos z at the point (-4,…

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Q: Give the Taylor series for sin x about xo = 2

A: To give the Taylor series for .

Q: . lim z--2 A) 1 A B /2x+5-1 x+2 B) 0 C) ∞ D) -∞ E) does not

A: we need to find out the limit."As per the rules, we are supposed to answer the first question and…

Q: 4. §11.5. Q10. Use appropriate form of the chain rule to find dw/dt. w = √√√1 + x2yz¹x; x = ln t, y…

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Q: Find where y is defined as a function of a implicitly by the equation below. 3 da 3y² - 5y-1 = r² =…

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Q: Solve the following differential equations using Exact method ху (2+ye Jdx + (x-2y) dy =0

A: we need to find out the solution of the exact differential equation.

Q: The following is the graph of y = g(x). Use this graph to compute the following quantities, or state…

A: Find the solution of all parts using the given graph

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

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Q: L'Hôpital's Rule does not help with the following limit. The expression keeps on cycling. Find the…

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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: Set up the definite integral required to find the area of the region between the graph of y = x² -…

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Q: Find the absolute maximum and minimum values of f on the set D where f(x, y) = x² + 4y² − 2x − 8y +…

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Q: 4 n ·1 I k=1 3k 4 3k+1

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