Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2 minimum maximum (x, y) = (x, y) = DNE

Q: using an appropriate su OTE: Enter the exact answer. 4 | - | dx - 4 (1 – 2x) ¹ +C

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Q: The equation of the tangent plane to the surface x² z² at the point (-2, 1, 3) is Select one: + 2y.…

A: To find the equation of tangent plane.

Q: A $120,000 mortgage was amortized over 15 years by monthly repayments. The interest rate on the…

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Q: Evaluate the integral and check your answer by differentiating. x² +8x4 1 x6 1² dx +C

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Q: The function f(x, y) = 2x² + 4y² + 2x³ has a local maximum at the point (0, 0). Select one: O True O…

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Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Chelsea received a loan of $1,300 at 5.75% compounded quarterly. She had to make payments at the end…

A: We need to find payments.

Q: If V f(x, y) = (x² - 1,√y-1), then f have two critical points (1, 1) and (-1, 1). Select one: O True…

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Q: Find the equation for an exponential function that passes through the pair of points given below.…

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Q: where R= [1, 2] x [-1, 2] is equal to Select one: None of them √ [₁3x²- (3x² - 2y), R 0 1 18 24

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Q: Which one is the set of all critical points of the function f(x, y) = x²y + x² - 9y+1? 2 Select one:…

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Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: After a large number of drinks, person has a blood alcohol level of 200 mg/dL (milligrams per…

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Q: 6. Find an equation of the tangent line to the curve at the indicated point: (t) = t cos(t), y(t) =…

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Q: What is the area of the right triangle with vertices at P(4,3 6), Q(-2. 0, 8) and R(1, 5, 0) ? O…

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Q: Find the center of mass of the lamina bounded by the graphs of the equations x = 64-y² and x = 0 for…

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Q: Let f(x, y) = x²y³, then Vf(1,2)= Select one: True False

A: Given problem:- fx,y=x2y3 Then ∇f1,2=16,12?

Q: Is the equality T ["(" true or false? Select one: O True O False 8r sin 0 dr d0 = 0

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Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) [ 1 Sketch the region R. b) Evaluate…

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Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 4 SS 0 X 08 2xydydx?

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Q: The value of the integral Select one: a. 2√2+1 3 b. None of these c. 2√2-1 3 2V/2 d. e 1 2 [²C x√√y…

A: Evaluating the definite integral

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: Given than [ f(x) dx = 4 and the following is NOT TRUE A B C [ f(x) dx = 8, which of [2f (a) dx = 24…

A: We know, ∫abf(x)dx=-∫baf(x)dx

Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞). Find all INFLECTION point(s) of…

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Q: Find the radius of convergence of the series. 5 OR=7 OR = 1/ OR=1 OR=00 OR=0 7"x" 1 (n + 1)"

A: We need to find radius of convergence.

Q: 2. Given a tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4). Express the volume…

A: Given:- A tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4).

Q: 1₂x (x + y) dA, where R is the region that lies to the right of the y-axis between the circles x² +…

A: We have to evaluate the integral.

Q: The Integral ffyr² dydx can be written as Select one: O So yx² dady Spa

A: Need to change the order of the integration and select the correct option. Given information: The…

Q: Is the following statement true or flase? Select one: True False 5 2 1² 1²0 2 5 = √ √ ² x dx) ( √ ²…

A: The objective of the question is evaluate the double integral and choose the correct option.

Q: ƒ7 In ()dx if sec¹ (3x) dx

A: Integration by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫ddxf(x)·∫g(x) dx dx

Q: The maximum rate of change of the function 1 f(x, y) = at the point (1, -2) happens in direction of…

A: I have find the direction and value of maximum rate of change of given function and say that given…

Q: Question 1 Consider the matrix A- - (a) (b = 64 -1 1 -1 0 3 -2 -2 2 1 Compute the adjoint matrix…

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Q: ition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the…

A: Please see the below picture for detailed solution.

Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Use the point on the line and the slope of the line to find three additional points that the line…

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Q: Question 2 [2 Consider the matrix B= = (a (t -1 2 1 -1 2 1 -1 -2 0 Use the cofactor exapansion to…

A: We have to find the determinant.

Q: A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being…

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Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

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Q: Find the gradient vector of the function f(x,y) =. Select one: O None of the others. - O O + 6xy,…

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Q: 33) (x5-2x4)4 (5x4-8x3) dx

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Q: 1. Find the gradient of the function f(x, y) = x² sin y.

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Q: The directional derivative of f(x, y) = xe + 2y at point (2, 0) in the direction of the angle = is:…

A: Given that fx,y=xey+2y at the point 2,0 and θ=π3 find the directional derivative

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person,…

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Q: 1. Given the graphs below: The blue graph is r=- =√√3 sin and the red graph is r = cos. Use a double…

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Q: The series 8 Select one: O True O False n=1 2 5" is a geometric series with r = }/1. -iin

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Q: Solve the given differential equation by undetermined coefficients. y" - 16y = 96 y(x) =

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