Find the gradient and maximum value at the given. point: f(x₁y) = Sy² at (4,5) X

Q: a) Find f'(0) if f(x) = 2x Give three digits past the decimal point. b) What is the slope of the…

A: To find the derivative of given function at the mentioned point.

Q: Find dz ди Z = fan ( auf dz av as fn. of u and if ),X = u Cos V, y = usinv? (y)

A: Solution will be given below.     ∂z∂u =partial derivative of Z with respect to u ∂z∂v =partial…

Q: Find the antiderivative for the given function. (Hint: Use inverse hyperbolic functions.) + C F dx…

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Q: B- Find the equation of the tangent line to the curve y = x² - 2x at x = 3

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Q: 7. Show that if f is a function of r only, then 0²ƒ(r) = f'(r) + ²ƒ'(r)

A: The given data is: Show that if f is a function of r only, then ∇2fr=f''r+2rf'r

Q: Use L'Hospital's rule to determine the following limit. Use exact values. 9ª - 82 lim x-0 x

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Q: Help with 2 c

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Q: The distance from (6, 8, 11) to the yz-plane is: A. 10 OB. 7 O C. 5 O D. 6

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Q: Find T, N, and x for the space curve, where t > 0. r(t) = (9 cos t+ 9t sin t)i + (9 sin t 9t cos t)j…

A: Please see the below picture for detailed solution.

Q: 625 242 A car traveling at 50 mi/hr. skids ft. If we assume the brakes provide a constant…

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Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

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

Q: Find dy dx using implicit differentiation. 6x² + 7y 4x + 2y² = 28

A: To find dy/dx of given equation.

Q: If z = ln(2x+y), x = u sin v, y = v cos u, find az/av when u = 0, v = 1. A. -2 B. -1 C. 0 D. 1 E. 2

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Q: dy Choose the expression equal to dx (Use implicit differentiation.) if sin(xy) = x²

A: Topic = Derivative

Q: A 5.3 ft tall man is walking away from a 30 ft tall lamp post. If he is walking at a rate of 2 ft/s,…

A: Let AB be the lamp post 30 ft in height.Let CD be the man 5.3 ft tall.Let x be the distance of the…

Q: The first term of a geometric series is 4. The sum of the first two terms is 7, and the sum of the…

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Q: Consider the following. y = 3x³ - 18x² +7 (a) Find the critical values of the function. (Enter your…

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Q: 1. Based on data from the US Census Bureau, the US population in 1990 was approximately 250 million…

A: Two points ( 10 , 250 ) ( 20 , 280 ) exponential growth of model y = y0ekt

Q: Find the limit. (If an answer does not exist, enter DNE.) lim X→ 8 X+8-4 X-8

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Q: In this problem, y = 1/(1+c₁e) is a one-parameter family of solutions of the first-order DE y'= y -…

A: Given y=11+c1e-xput  x=0 and y=-17we get -17=11+c1e-0-17=11+c11+c1=-7c1=-8

Q: please

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Q: 98t √√²+1 answer, do not use decimal approximation. (Assume units of meters and seconds.) Use the…

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Q: Given f(t) = 6 t + 7 what is the rate of change Δf/Δt = ?

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

Q: 2. 1 1 x² + y² y² = 2 show that d²y dx² انه انه xz

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Q: = indefinite integral X 2²-1 dx

A: ∫x2x2-1dx

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: Given f( x, y ) = 3x2 + xy2 -4x + 1

Q: Find the integral

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Q: Sketch the region of integration and change the order of integration. 3 In(x) f(x, y) dy dx f(x, y)…

A: Given initegral:- ∫13∫0lnxfx,ydydx

Q: g. y = u² + u³, u = ³ - 4v, v = 3 - x², x = 2 u5

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Q: 1 1 Jo x-1 dx

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Q: Suppose a baby food company has determined that its total revenue R fortits food is given by R = -…

A: Given : Suppose a baby food company has determined that its total revenue R forits food is given…

Q: Determine the remainder when the function y = 2x5-7x4-13x3 - 5x² - 27x + 10 is divided by each of…

A: According to our guideline we are supposed to be solved first three sub-parts of the question, if…

Q: Use the​ price-demand equation to determine whether demand is​ elastic, inelastic, or has unit…

A: Given that x= f(p) = 48000 - 40 p2    and p= 19 The elasticity of demand is a measure of consumers'…

Q: Find slope of secant line from points [2,-10] and [5,-8]

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Q: Suppose an oil spill in the ocean formed a circle and was growing at a rate of 57 feet2/minute. When…

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Q: What is the standard form equation of the parabola given the focus and vertex. vertex: (-8,1)…

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Q: dy 1. Use implicit differentiation to find dx for the curve xy² + x² = y +1

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Q: Evaluate the indefinite integral Ssec² (x) dx

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Q: In our discussion about Fibonacci sequence, we said that Fibonacci numbers occur in the species of…

A: see below the answer and explanation

Q: Choose the expression equal to (Use implicit differentiation.) E dx In(x + y) = x

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Q: Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) x² - 16 X+4…

A: Given,          limx→-4x2-16x+4

Q: A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the…

A: Given: a = 0 , b = 5  , n = 10 ∆t = (b-a) / n => (5-0)/10 = 0.5 ∆t = 0.5  n = 10

Q: Find the derivative of f(x) = = (2x-4) (3x+6) x-1

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Q: Find the equation of the tangent line to the graph of f(x)=−4xln(x+1) at x=5 Answer:y=

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Q: Problem to Work Out extbook problem 3.1.67: "FLIGHT OF A MODEL ROCKET The altitude (in feet) of a…

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Find the average value of the function on the given interval. The graphs are provided for you to…

A: We need to evaluate the average value of the given functions on the given intervals 1. fx = -x2-2x+5…

Q: o evaluate the expression.

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Q: B. Find all the rational zeros of each 28. 2x³ + 9x² +7x-6=0 29. 2x³ + 16x² + 14x = 0 30. 6x³ +…

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Q: (b) Find the areas under the graphs of f and g from x = 1 to x = t and evaluate for t = 10, 100,…

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