Check that the point (1, 1, 1) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y, z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1, 1, 1). vector normal = tangent plane: x² - y² + 4z² = 4

Q: Continuing with the same graph of f(x), which value is the greatest: f(5), f'(5), or f(6) -f(5) ?…

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Q: Write Z₁ and Z2 in polar form. 11π - 4( cos( 11 ) + sin ( 1 )) i 11π 6 Z1 = Z2 Z1Z2 = Z1 Z2 Z₁ =…

A: you should write a bracket

Q: 2+2+2+1 de

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Q: Solve the initial value problem. Chapter 6, Section 6.2, Go Tutorial Problem 16 Find Y (s). Y(s) =…

A: We have to find the Y(s).

Q: Consider the function f(x) = 1 − 6x², − 5 ≤ x ≤ 2. The absolute maximum value is and this occurs at…

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Q: 50. y = x¹/x

A: To find : Derivative of the function y=x1x Take logarithm to both sides, we get logy=1xlogx …..(1)

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Q: H f(x) = 2x²+x-6 (a) Express fin standard form. f(x) = (b) Find its vertex and x- and y-intercept(s)…

A: We have to find out

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Q: Sketch the region of integration and evaluate the following integral. [x² dA; R is bounded by y = 0,…

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Q: Evaluate the triple integral E 2x dV where E = {(x, y, z)/0 ≤ y ≤ 2,0 ≤ x ≤ √4-y²,0 ≤ z≤y}

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Q: A company that produces cell phones has a cost function of C = 5x² - 155x + 6619, where C is the…

A: Given query is to find the number of units need to be produced to minimise the cost.

Q: Find the inverse Laplace transform L¯¹{F(s)} of the function 2 F(s) = s² + 5s 6 NOTE: The answer…

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Q: Determine the area of the region bounded by two the curves f(x) = 2²-26z+72 and g(x)= 13z +36.

A: To find the area of the region bounded by the two curves.

Q: Find the derivative of the function. -0 f'(x) = f(x) = (2x - 5) 4(x² + x + 1)5 x

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Q: Suppose a product's revenue function is given by R(q) = is units sold. Find a numeric value for the…

A: Given query is to find marginal revenue.

Q: If y=xe, then find d" y dx"

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Q: 2 3...... 2 y...) + Xdy =0 where yo...

A: Given differential equation  (2xy−1)dx+x2dy=0

Q: The graph of a function is shown below. Over what interval(s) of x is the function decreasing? V

A: Given query is is to find the interval where function is decreasing.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

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Q: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.) r = 7 +…

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Q: Find the partial derivatives of the function fz(x, y) = fy(x, y) = 1 f(x, y) = 4x 2y 1x + 2y 1

A: Given: Now, fx(x, y)=∂ ∂ x4x-2y1· x+2yTreat y as a constant             =∂ ∂ x4x-2y1· x+2y-∂ ∂ x1·…

Q: The weekly demand for Xbox Math-Hero video games is given by where x is the number of Xbox video…

A: I am attaching image so that you understand each and every step.

Q: 5) Determine the time it takes an amount of money to triple if compounded continuously

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Q: Find the derivative of the function below. h(x) = x tan (8/x) + 1 dh

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Q: d²y (2) Check that y = sint satisfies the differential equation dt2

A: We have to solve

Q: Based on the data shown below, calculate the regression line (each value to two decimal places) y =…

A: Here for the given values.The best fit values for the regression line are- Slope =1.106 ± 0.08099…

Q: r> 0 r< 0 (4₁-2-3) (r, 0) (r, 0) = X X

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Q: A particle moves along the x-axis so that at time t≥ 0 its velocity is given by v(t) = 6t² − 24t +…

A: We have to determine the intervals when particle is moving right.

Q: Given the given cost function C(x) = 7550 + 780x + 1.7x² and the demand function p(x) = 2340. Find…

A: Find the profit function using the given functions for x units

Q: Find the equation of the tangent plane to the surface z = cos(5x) cos(6y) at the point (2π/2, π/2,…

A: The equation of the tangent plane to the surface ?=?(?,?) at the point (?,?,?(?,?)) is…

Q: 1. Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect…

A: Please see the below picture for detailed solution.

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = t³ – t² –…

A: Topic- Application of derivatives We are given x(t)=t3-t2-16tWe know…

Q: Charles 'n Marge sell custom-build cabinet units for motor homes. The function P(x) = 2x² + 700x -…

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Q: When using the - definition of limit to prove lim f(x) = L, you must show that for every x→a € > 0,…

A: We need to choose correct option.

Q: Let f be the function with derivative given by f'(x) = sin x + cos (2x) - for 0≤x≤. On which of the…

A: NOTE: Refresh your page if you can't see any equations. . the derivative of the function is given by…

Q: Find the maximum value of f(x, y) = -7x²+2x+4y² +4 on the region x² + y² ≤ 25. Enter an exact…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Graph of the region is given and it is rotated about x-axis, We have to find its volume.

Q: Let z = f(x,y) = 15x² - 25xy +9y². Find the following using the formal definition of the parti əz ду…

A: All the subparts are solved below

Q: If $14,000 is invested and interest is compounded quarterly, determine the amount of the investment…

A: A=P1+rnnt ⇒A=Amount at time t⇒P=initial amount ⇒r=rate of interest ⇒t=time in yearsn=compounded…

Q: f(t) 1 10 2 55 Given this limited data, what is the best estimate for f'(2)? 3 80

A: Given:  t 1 2 3 f(t) 10 55 80 To estimate: f’(2)

Q: Exercise 2 The given limit lim h→0 (3-(2+h)²+2)- h Definition of the derivative represents the…

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Q: 5. Find the inverse function of f(x) = 3x - 7. 3.2.1) mont noita ovitostjd a (ewors diw) Jou Maitsa…

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Q: Consider the function f(x) = 4√√x + 6 on the interval [2, 5]. Find the average or mean slope of the…

A: Given, f(x)=4x+6

Q: Give your final answer in interval notation. Find (by hand) the intervals where the function…

A: The given function y=x3-48x+1 We have to find its increasing and decreasing intervals.

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Q: Find the equation of tangent xªy-xy²= line to 1=-2 at (-1,41)

A: The given equation is; x4y-xy3=-2, (-1,-1).

Q: List all the primes between 20 and 40 in increasing order (in the form 2,3,5,7,9,11). A/

A: I am attaching image so that you understand each and every step.

Q: Find the equation of the line tangent to the curve x4 + 4y4 = 5 at the point (1, 1).

A: