Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate f(3.1, -1.04).

Q: The Cartesian coordinates of a point are given. (a) (-6, 6) Find the following values for the polar…

A: Polar coordinates

Q: Solve the given differential equation by separation of variables. xy + 5x - y -5 xy - 2x + 6y - 12…

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Q: The volume of the solid generated by revolving the region bounded by x² = 4y and y² = 4x about y = 4…

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Q: ∞ ΣΕ - (x – 6)η n(5)n

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Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: n=0 In(n + 4) n+4

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Q: For a function h(x) we know that h(50)=68 and h’(50)=-5. Estimate the value of h(53)

A: Topic = Functions

Q: 10. f(x)=(x+2)(2x-3) 11. 4x-2x+1

A: To find the derivative of the following functions

Q: following

A: Please refer to the image below

Q: dy d²y Find and dx dx² x=t² + 4, y = t² + 9t 11 dx d²y dx² For which values of t is the curve…

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Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

A: We will find the derivative of given function as shown below

Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (9x (9x - 8)…

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Q: Question 9. A circular helix in ryz-space has the following parametric equations, where ER. I(0) = 4…

A: Given : x(θ)=4 cosθy(θ)=4sinθz(θ)=3θ

Q: Use counting arguments from the preceding chapter. The seven contenders in a horse race at Aqueduct…

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Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

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Q: Use the method of Lagrange multipliers to find the maximum and minimum of the function f(x, y) = y²…

A: Solution is given below:

Q: 2T Rewrite cos x + 3 in terms of sin(x) and cos(x)

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Q: Evaluate 6252 6251 6250 6254 6253 Ads, where C is the right half of the circle x² + y² = 25.

A: To evaluate the given integral.

Q: Evaluate e √ √x +4-2 √√x²-16 2√x 4+4ln√√x+4-√√x−4+C B 2√x−4+2ln(√x+4-√√x-4)²+C…

A: I=∫x+4-2x2-16 dx =∫x+4-2x+4x-4 dx=∫x+4-2x+4x-4 dx Lets substitute u=x+4⇒dudx=12x+4=12u⇒2udu=dx also…

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 6x²+x-1 Ilm…

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Q: Find the component of u = 2i + j − 3k that orthogonal to v = 3i – j, then verify your result.

A: This question can be solved using the concept of component of vectors.

Q: Find Select the correct answer below: 33 0 d = - = where y is defined as a function of x implicitly…

A: The objective of the question is determine dy/dx.

Q: 2. What is the degree of the function g(x)=-2x(2x-1)(x² + 1)²?

A: The given function is; g(x)=-2x(2x-1)(x2+1)2.

Q: Find the area of the surface over the given region. Use a computer algebra system to verify your…

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Q: Write the product as a sum: 20 cos(136)sin(116) =

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Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2-2 at the point (3,1).…

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Q: Consider the following function and graph. f(x) = x + 2 1 -3+ Determine whether f(x) approaches ∞ or…

A: In this question, we want to find the left hand limit and right hand limit of the function.

Q: Complex Numbers. 1. Evaluate the following. Express all final answers in rectangular form. a.…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

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Q: Ιπ 10. State the exact value of tan- 6

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Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: Evaluate the limit. Select the correct answer below: O + O-3 03 0-1/3/2 0 1/1/012 The limit does not…

A: Given, limx→3x+1x2-2x-3

Q: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: For the following exercises, the given limit represents the derivative of a function y = f(x) at x…

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Q: The

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Q: For the given demand equation, differentiate implicitly to find dp/dx. ) 40p2 - 300p + 612 = x

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Q: (Dº − 4D³ +3D³),y = −27

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Q: Determine the value of k for which the direction vectors of the lines x+3 Z = y = -1 are…

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Q: Find f'(x) and find the equation of the line tangent to the graph off at the indicated value of x.…

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Q: Given that n=0 x = 1 1-x Identify its interval of convergence. The series is convergent from , left…

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Q: Find f'(x). f(x) = (3x + 10)7 (1 − √) 3(3x + 10) (1 − √x)³ f'(x) = 21(3x + 10)6 (1-√) f'(x) = 7(3x +…

A: Given data÷ fx=3x+1071-x6 Find the first derivative f'x. Useful formula ddxxn=nxn-1…

Q: Use partial fractions to find the power series of the function: 8 n=0 11x² + 629 (x² + 64)(x² + 49)

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Q: Find the derivative. F'(x) if F(x)= (ex² -3) ² F'(x)=

A: ddxex7-32

Q: Solve 6 sin X = π X = 2 for the four smallest positive solutions

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= X-2 9x-4…

A: topic- equation of tangent line to curve

Q: ∞ Σ η=1 7η + 3η gn

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Q: slope

A: Please refer to the image below