Use a tangent plane at (-6,-4) to approximate the value of the following function at the point (- 5.9, - 4.1): - 2x² - 4y² +7z = - 101 Present your answer accurate to 4 decimal places.

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

A: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: (a) Evaluate the following. If the limit does not exist, explain why. lim f(x) = 3 4-0 lim f(x) = 1…

A: Graph of the function is given, we have to find the given limits.

Q: Find the next term in the sequences 5,24,7,48,15,x.   Find x. Please show all the steps of the…

A: Solution is given below:

Q: Part A: Use exact area calculations (not Riemann sums or the FTC) to evaluate of the following…

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Q: cos 20 im tan e 9. |N 2

A: Solve the given

Q: The solution of the differential equation (ex + 1)ydy = (y + 1)e* dx is: y = (ex + 1)(y + 1) e = C(y…

A: Given differential equation, ex+1ydy=y+1exdx......(i)So, exdxex+1=ydyy+1.......(ii)

Q: (a) When he is 3 meters from the base of the light, at what rate is the tip of his shadow moving?…

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Q: Find the domain and range of the following graph in interval notation. 5+ 4 -4 -3 -2 구 3 2 1 dy 1 4…

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Q: (1 + x²)y' = x¹y¹

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Q: 1. Use partial fractions to evaluate the following integrals 5x-7 S x²-3x+2 a. dz b. y+4 +y dy C.…

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

Q: 5. Using implicit differentiation, find dif dx 2 x² + xy + y³ = 0.

A: Topic = Derivative

Q: The function f(x) = √√2x − x² is given graphed below: (A) Starting with the formula for f(x), find a…

A: We can solve this as follows:

Q: X lim x→0 √1+x -√1-x

A: To find the limit of the given function as x approaches to 0.

Q: answer

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Q: e equation2x=y² is a separable differentiable equation. dx

A: Given: 2xdydx=y2

Q: 1- y²dx + √√√1-x²dy

A:

Q: The solution of the differential equation (e* + 1)ydy = (y + 1)e* dx is :

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Q: Find the slope of the tangent line to the graph of the function at the given poi f(x) = 3 at (1, 2)…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 6 √x dy = y = 9√√x +

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

A: Given line x=2t, y= t − 3, z = 2t + 2 That is , r=(-3j+2k)+(2i+j+2k)t And given point (7,-6,5)

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: Question 35 f 16x (2x²-3) 4 + c O4(2x² - 3) 4 + c O4x (2x² - 3) 4 + c O 48(2x2 - 3)2 + c Evaluate…

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Q: x²y' = 4x² + 7xy + 2y²

A: We use homogeneous method to solve the given differential equation.

Q: 9. y(cos³x) (cos²2y)

A: We are asked to find the solution of the differential equation

Q: (1) Find the average rate of change for the function 3x³ - 2x £5 on the interval [=-2, 6]. f(x):

A: We have to find out average rate of change

Q: lim X-> - -2x + 25x²-2 x+3

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Q: has

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Q: Directions: definition Find the derivatives using the of limits (4-step Rule). Show each step from…

A: Given: y=9-7x1-xTo find:The derivative of the function

Q: C. Write the equation of a circle in general form. Determine the center & radius. Sketch the graph.…

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Q: 1. State whether f and g represent the same function. Explain your reasoning. x² - 1 x+1 1 (a) f(x)=…

A: We can explain the answers in the below steps.

Q: Find the domain of the composition (fog)(x) given f(x)=x²-1 and g(x)=√√x²-4. If possible, find…

A: If f : A → B and g : B → C then (f∘g) : C → A defined by (f∘g)(x) = f(g(x)) for all x belongs to C.

Q: Calculate how many liters (and gallons) of water arelost in 1 month by a toilet or faucet that leaks…

A: The faucet leaks 2 drops of water per second. one liter of water=3500 drops. 1 liters=0.265 gallons.

Q: The solution of the differential equation (e* + 1)ydy = (y + 1)e* dxis :

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Q: Use the graph of f to find the largest open interval on which fis increasing, and the largest open…

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Q: Find all solutions to the equation cos(x) = √√3 2 in the interval [7, 2ë].

A: We can find the answer in the below steps.

Q: Given the graph of f(x), find: lim f(x) A. B. 8. lim f(x) X->-2* c. f(6) -12-10-8-64-2-1

A: We have to find out limit from graph

Q: Question 3 A (B) ) Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ? 3x²y…

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Q: DETERMINE THE FOLLOWING: Differential Equation GIVE EXAMPLES AS WELL BUT MAKE SURE IT IS ORIGINAL…

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Q: Find the derivative of y = 25 Select one: O a. O b. du O c. O d. dy e. || -(2x-5)cscrcotx-2cotx…

A: Solve for the derivative

Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

A: Recall: Disk method

Q: $ 3 months $

A: We will find the required.

Q: A graph of Y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

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Q: (In x-4) dx x(ln² x+3)

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Q: Evaluate 6-2x-3y (2 2x dzdydx =

A: Topic = Integration

Q: If f(a, b) = eab (ab + a), show that fûû(a, b) — àƒÂ(a,b) = a²eab

A: We can solve this as follows:

Q: Find the domain of the following function. f(x) = ln(9-√√x-2)

A: Topic = Functions

Q: 15. Find f(x) using the limit definition of the derivative. f(x)=√2-x In the answer box, enter the…

A: We have to find derivative

Q: K(x) ++ext H(x) d Identify the graphs above as the origninal, first derivative, second derivative,…

A: We have to identify the graph of the function and it's derivatives

Q: Use the root test to determine whether the series converges or diverges. If the test is…

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