1. The point (-2, 5) lies on the circle whose center is at (-1,-3). Write the standard form of the equation of this circle.

Q: Find the power series representation of the following function f(x) = ln(1+x)

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Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find the general solution of the differential equation. y(5) — 11y(4) + 29y"″ − 11y" + 28y' = 0.…

A: Let's solve given diffrential equation.

Q: 2. Determine the intervals of increasing and decreasing, critical numbers, and classify relative…

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Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t², y = 9+ 4t³,…

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Q: 8. Find the local maximum and minimum values and saddle points of the function f(x,y)=2x + 4y +3x²…

A: This is a problem related to maxima and minima. Please follow the procedure given below.

Q: x 5. r(x, y) = ln (x + y)

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Q: (x + y \(xdy+ ydx)– xy(xdx+ydy)=( +y²

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Q: f(g(x)).

A: f(g(x)) = 25/x2  provided the answer in step2 with solution

Q: ! Using an appropriate substitution, the integral dx 36-(2x + 2)² is equal to sin-¹(x + 1) + C the…

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Q: For the graph below, identify a restricted domain for which the function has an inverse that is also…

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Q: The piecewise function /(x) is graphed below. Use geometric formulas to evaluate the following…

A: First we find f(x) , Here in interval -7≤x≤-1 f(x) is semi circle, whose center is at (-4,0) and…

Q: Let the transformation in and the appropriate order of how to make a graph of y= -4F(1/5(x-1))-3…

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Q: Find the differential dy of the given function. y = In√√/9-x² dy =

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Given f(x) = 5x² + 2x + 7, find ƒ'(x) using the limit definition of the derivative. f'(x)=

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Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (x² - 37) = -1…

A: This is a problem related to limit calculation. Based on epsilon-delta limit we will answer.

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. in 19 lim…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: We have to find the slope of the tangent line to the polar curve  r = cosθ3 at the point θ=π.

Q: (a) Show that the function f(x) = x² 2 n! n = 0 is a solution of the differential equation f'(x) =…

A: The Solution is given below

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. -7t y…

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Q: Determine whether the following series converges or diverges: 2. 1. +00 Σ n=1 1 + sin2n] 10n +00 ΣΕ…

A: We need to determine whether the given series converges or diverges

Q: or the graph below, identify a restricted domain for which the function has an -2 YA 8- 2- 0 -2- 2 6…

A: Topic:- calculus    Definition :-  The domain of a function f(x) is the set of all values for which…

Q: W -5 -4 -3 -2 -1 3 2 1 2 13 4 5 The function graphed above is: Increasing on the interval(s)…

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Q: 15. Verify the identities: a) csc x -sin x = cos x • cotx b) tan²0 1 + sece 1 - cose cose

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Q: Suppose f(z) represents the total number of children that have a symptom, and z is the number of…

A: We can answer both the question as below.

Q: Use numerical or graphical evidence to determine the left and right hand limits of the fund |32 -…

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Q: Q.7 Find the eigen vectors of the matrix: 1-(1 2) Your answer Q.8 Find the maximum and minimum…

A: As per the request of the student , (7) The matrix is given as , A=5412

Q: Find the gradient of the function at the given point. Function f(x, y) = x² + 2xy Vf(5,2)= (No…

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Q: What is the equation of the tangent line at 3x+1 0₁ = 1² of f(x) = ² 0, 2 X-2

A: The equation of tangent is :

Q: Find the gradient of the function at the given point. g(x, y) = 9xex/x, (17, 0) Vg(17, 0) = (No…

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Q: K If f(x) = x² + 7x and g(x) Answer = 51 find g(f(n)). g(f(n)) IL

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Q: *3. The dimensions of a rectangular solid are 8 by 4 by 4x+1, and surface area of the rectangular…

A: We have to find value of w.

Q: We are trying to prove the following limit. 1 Suppose that we have found a value of & such that e =…

A: According to the ε-δ definition of limits says that the limit of f(x) at x=c is L if for any ε>0…

Q: Find the exact length of the curve. x = 1 + 12t², y = 1 + 8t³, 0≤t≤4

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Q: Given the system of linear equations below, determine the value of a, b, and c using CRAMER'S RULE

A: The solution is given below

Q: A window has perimeter 10 m and is in the shape of a rectangle with the top edge replaced by a…

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Q: . A rectangular pen is built with one side against a barn. If 2300 m of fencing are used for the…

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Q: 1.3 Let f(x) = Use interval notation to indicate the domain of f(x). Note: You should enter your…

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Q: Find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye⁹², P(2,…

A: Given :gx,y,z=xye9zP2,2,0, Q0,0,0

Q: trigonometric substitution 2 X (9-x² -dx

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Q: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles.…

A: Solution is given below:

Q: A rectangular page is to contain 89 square inches of print. The margins on each side are 1 inch.…

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Q: A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is…

A: Given :- The shape of the tunnel = One-half sine curve cycle The height of the road at its highest…

Q: The photic zone of the ocean is also known as the sunlight layer. It is the region in which phyto-…

A: This is a problem related to variation in photon emission curve. Please follow the general procedure…

Q: 5. For y = -ln(x), find the value of x where the slope is a) x = − 6 b) -In(6) d) Does Not Exist

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Q: Mixed Partial Derivatives In Exercises 55-60, verify that way 55. w = In (2x + 3y) 57. w = xy² +…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 1 dy = y = 5 (4x-1)² X

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Q: Finals - Research All Formula in Integral Calculus.

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…