Find equations of the tangent plane and normal line to the surface z + 16 Tangent Plane: (make the coefficient of z equal to 1). Normal line: (16, +t( 3 1). re" cos z at the point (16, 0, 0). 0.

Q: Find lim(x-4) a. x-3 b. x→3 1 3 - (x-3) N|♡ 3

A: Topic = Limits

Q: Consider the following. y = x² y = 6-x 4 (a) Find the area of the region by integrating with respect…

A: Note: Since you have asked multiple questions we will solve the first question for you. To get the…

Q: If √ (2-4) (2 + 6) dr = Adr 2-4 Bdr +6' then A+B =

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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)

Q: f(x,y,z) = 4x5+2xy-4z4 f(x.V.Z) =

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Q: #21

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Q: Find the Linearization L(x) of the function at a. a) f(x) = x^2 -x+2, a=3.

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Q: Farmer Alex has 32 llamas each of whom needs 1000000 square feet of grazing area. He wants to…

A: Topic = Algebra

Q: Solve 4X 64 X+3 16 Solution set =

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Q: Write an equation for line L in point-slope form and slope-intercept form. L is parallel to y = 3x.…

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Q: A light source is located over the center of a circular table of diameter d = 12 feet (see figure).…

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Q: Find the equation of the line tangent to the curve 8x4 + 8y² = 16 at the point (1, 1).

A: To find the equation of the line tangent to the curve 8x4+8y2=16 at the point 1, 1.

Q: 1. Find a parameterization of the tangent line to r(t) = (- sin(2t), t², cos(2t)) at the point (0,2,…

A: Given :- rt=-sin2t,t2,cos2t

Q: Compute the derivative of the given function. sin ¹(³+4) O O O d dx d dx d dx [sin ¹(x³ + 4)] = [sin…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. IRL -144 yz dx dz dy =

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

Q: (бх+34)

A: The given expression is 8x+3410. Formula used: Binomial expansion formula is :…

Q: 3 x³ - 2-x. If ƒ (4) = 6 and dy = (f(u) +3.x)² an and u= x -2 = 18 when x = 2, find f'(4). Let y =

A: NOTE: Refresh your page if you can't see any equations. . . take derivative

Q: Using the same graph of f(x), what is lim f(x) ? X-2 1. ANL 0 2 3 2 -1- -2+ -2 doesn't exist -1

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Q: Evaluate the integral R --²dA where R is the region bounded by the semicircle z = √4-y² and the axis…

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Q: Use implicit differentiation to find y² + 4x³ = 8y - 5x² dy dz z(5+6x) y-4 da X

A: Topic = Derivative

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: Given the polynomial y = 3x³ +21x² +31x + 2, • list the possible rational roots: 2 2 1,-1,-1,- 2,-2,…

A: The given polynomial y=3x3+21x2+31x+2 We have to find the all possible rational roots of the…

Q: on given by P(q) = -0.02q² +5q-31, where and produced, and P(q) is the total profit, in of…

A: Here profit function is given to us.

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: to Use logarithmic differentiation And the derivative, (ar ²-1) 5 -f(x)=√√√²+3x-1

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Q: Differentiate. y' = || Y = 7-tan(x) y X

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Q: A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the…

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Q: Numerically estimate the absolute extrema of the function f(x)=x4-28²-32x+1 on the interval [-1,1].…

A: We have to find the absolute minima and maxima.

Q: In an extensive study of cost functions for 40 firms in Great Britain, it was found that if x is the…

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Q: Show that (csc(x)) = -csc(x) cot(x). d dx d dx -(csc(x)) H = = d dx sin²(x) 1 sin(x) 1 = -csc(x)…

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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: Determine where the graph of f(x) = 2x³ + 27x² − 45x-60 is concave down. f(x) is concave down where…

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Q: nd a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Suppose a product's revenue function is given by R(q) = - 8q² + 900q, where R(q) is in dollars and q…

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Q: O 62 sin² (1) da = In(sin(x)) + 6 In(sin(x)) In(sin(x)) + In(sin(x)) (Apply integration by parts…

A: ∫u(x)v(x)dx=u∫v(x)dx-∫ddxu(x)∫v(x)dxdx ∫cotxdx=ln|sinx| ∫csc2xdx=-cotx

Q: Find the first partial derivatives of x - y x+y f(x, y) = af -(1, 1) = д х of ду -(1, 1) = = at the…

A: Concept: Let's say we have a function f(x, y) that depends on the values of two independent…

Q: dz ds A. Use the chain rule to find dz მყ dz Ot || dz Ot Suppose z = =x² sin y, x = = (-5,5) = and…

A: Please see the below picture for detailed solution.

Q: XYZ Things Inc. produces and sells pressure washers per year at $p per pressure washer. The demand…

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Q: Solve the initial value problem. Chapter 6, Section 6.2, Go Tutorial Problem 16 Find y(t). O O O y…

A: The given differential equation is; y''-2y'+2y=e-t ; y(0)=0, y'(0)=5.

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: dy dx x5(x + y) = y²(6x - y) X

A: Topic - application of derivatives

Q: The graph of f is given in black. Which of the blue dotted graph is the graph of f'(x)? (B) f(x) INN…

A: We know that when the function is decreasing, its derivative is negative and when the function is…

Q: Determine the value of an investment in the amount of $4000 that matures in 4 years and pays 7.5%…

A: Let's find value of amount after 4 years in each given cases.

Q: PROBLEM - Standard form x+5x11 =y Vertex form Axis of symmetry Opening (upward or downward) Type of…

A: Vertex form of the prabola : y =ax-h2+k ; where (h,k) is the vertex of the parabola .

Q: If f(x) = sin(x¹), find f'(x) Find f'(2) (round to 3 decimal places)

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Q: If f(t) is the number of people that come into an ice cream shop on a hot day, as function of time…

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Q: Find the absolute maximum of the function f(x)=x²-1x +4 on the interval [0, 2]? (a) The absolute…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1.954 as follows: Let f(x)=x4 . The…

A: need to find out by linear approximation the value of 1.95⁴

Q: The composite function theorem allows for the demonstration of which of the following statements? O…

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Q: BOTTOM LINE QUESTION Find the exact area under the curve f(x)=x²e* from x=0 to x=2. Show your work…

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