Let f (x, y) = 3x – 2²y. x = -t, y = s + 2t dz dz Use an appropriate chain rule (involving , , etc.) to find at the point s = 0, t = 1. Be sure to use a chain rule. Show all your work and answers on your own paper. You may leave the box below blank.

Q: Use the laws of logarithms to expand and simplify the expression.

A: Simplification

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: 6) Find a) given: y=-+ (3x' +27) (use product rule) 2x² +5 given : y = b) (use quotient rule) 3x-4

A: Since you have posted multiple questions i can do first question (with both subparts)as per our comp...

Q: a) lim x-3 x+1 x2 – 4x + 4 b) lim x-2 x2 +x - 6 y? – 4y – 21 c) lim y-7 3y2 – 17y – 28 t3 +t2 – 5t +...

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant an...

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A: Question- Find the point of diminishing returns (x.y) for the function R(x) , where R(x) represents ...

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A: topic- binomial series

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A: We have to explain the difference between the derivatives as in when we  use each one and give examp...

Q: Sketch the region bounded by the given curves, then find its area. x = 8 - y^2, x = y^2 - 8

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Q: b) | sin “ xdx d) [ /tan x sec“ ,

A: Given problem:- b.   ∫ sin4(x) dx  d.   ∫√tanx sec4(x) dx

Q: 2x2 Use the guidelines to sketch the curve y = - 1 A. The domain is {x | x? - 1 + 0} = {x | x * ±1} ...

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Q: The monthly water charge for a farmer based on his consumption can be calculated using this function...

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Q: Find the sum of the infinite geometric series. If an answer is undefined, write UNDEFINED. - 216/49...

A: To find the sum of the geometric series.

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A: Speed

Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

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Q: solve for 0 ≤ Θ < 2pi    ,                                            Θ = theta -cosΘ+sinΘ=1

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Q: c notation and fractions where needed.)

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Q: J Arctan(x)dx xArctan(x) -In(1 + x²) + c

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Q: Which of the following statements is false for functions f(x) and g(x) and constant c? O (c - f(x)) ...

A: Given query is to find which statment is false.

Q: Find the area bounded by the curve 2x + 4x + y – 0 and the line y + x = 0 1 1.125 1.525 1.823

A: We will find the area bounded by the curves. 

Q: 38. At what value of x should the function f(x) = In(x – 4) approach to so that f(x) will be as smal...

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Q: (y – 3)² (x + 1)? 1 36 The exact distance from the center to each focus is:

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Q: Define f(x, y) 2x2 + y? – 2xy + 6x. Find all critical points of this function, and determine, for ea...

A: The given function is: f(x,y)=2x2+y2-2xy+6x

Q: , for x 1 -X Discuss the contuniuty of f andf".

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Q: f(x) = ex, a = 1 f and T, on the same screen. y y 3 -1 -1 1 -4 -3 1 y

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Q: Suppose that f(0) = -5 and f'(x) < 4 for all values of x. Use the Mean Value Theorem to determine ho...

A: Question- Suppose that f(0) = - 5 and f'(x)&lt;=4 for all values of x. Use the Mean Value Theorem to...

Q: 9. If 8000 dollars is invested in a bank account at an interest rate of 6 per cent per year, compoun...

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Q: Sketch the regien enclosed by the given curueS Y = xe*

A: Question- Sketch the region enclosed by the given curves: y = x2 e(-x) &amp; Y= x e(-x)

Q: Which of the following is a solution of the differential equation xy' +y = 4x? y = 14x-1 - 2x %3D Oy...

A: We can solve this problem by applying the concept of linear differential equation.

Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) < 0 and f"(x) <...

A: Given problem:- To select graph  with conditions  f'(x) &lt; 0 and F"(x) &lt; 0 for all x f''(x)&gt...

Q: Undelined

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Q: function f(x) = x² ose x-coordinates are -2 , 0, and 1. 2x and draw the tangent lines to the gr 10 4...

A: We will draw the graph and the tangents. 

Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an ...

A:

Q: uation of the plane that contains the lin y = 5+3t, z =-1-4t

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Q: Determine which of the vectors is (are) parallel to z. Use a graphing utility to confirm your result...

A: If z is parallel to a vector u then u =lemda z 

Q: Recall y" Second Derivafive Analy'sis goals O track intervals of positive $ = -6x(x²_ax+4) (xta)? (x...

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your a...

A:     L-15s-8s2+16=L-15ss2+16-8s2+16=5L-1ss2+16-8L-11s2+16=5cos4t-8·14sin4t=5cos4t-2sin4t

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 8 6 6 y 4- y 4...

A: This is a problem of integration. Based on the x and y limit we will sketch the region. 

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-...

A: Solve by using graph

Q: etermine if g is differentiable at x = 0 if -1 COS if – 1 0. x + cos x

A: Differentiable

Q: Write the equation of a parabola whose directrix is y = - 0.75 and has a focus at (– 8, 8.75).

A: Let's find. 

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A: Find your answer below 

Q: 3x dx 1+r4

A:

Q: Part C lim, -3 h (x), if h (x) : Vx² + 6x + 9 x + 3

A: