Let y be a function of x and supposex=In(x²-y2). What is the correct value for the derivative of y with respect to x?

Q: The magnitude of the rate of decay of a radioactive material is 0.71 times the amount of the…

A: The magnitude of the rate of decay of a material is 0.71 times the amount of the material present.…

Q: Use your answer above to approximate 3 radical 0.99 + In(1.01). Write your final answer as a…

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Q: Solve the following initial value problem using (Laplace Transform) 9y''-12y'+4y=x4 y(0)=2…

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Q: Find the coordinates of any local and absolute extreme points and inflection points. y = 2x3-9x² +…

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Q: (part 1 of 4) Determine the distance of the point Q(3, 4, -2) From the y-axis. 1. distance 2.…

A: According to the company's guidelines, I can oy answer one question since both the questions are not…

Q: A ladder is leaning against a vertical wall. Due to the smooth ground, the foot of the ladder is…

A: Given horizontal distance from the wall = x vertical distance from the wall = y

Q: 1 √√(x + y + z)ds, where C' is parmeterized by Find the value of integral r(t) = (15 sin(t), 2√14…

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Q: Q-2: a) Let f(x) = x³ - x²-24x - 4. Find the intervals at which f is increasing or decreasing.

A: As per the rules we are supposed to answer the first question and rest other can be reposted.

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: Given function, fx=x2-3x-4x-2

Q: 8√x √x dx

A: We need to solve∫8xxdx

Q: Given the hyperbola with the equation y² – 9x² - = -9, find the vertices, the foci, and the…

A: We will find the required.

Q: TOPIC. CURVE SKETCHING f(x): = Intervals a. Find f'(x) and f"(x). b. Determine the following…

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Q: Solve the problem. Suppose a business can sell x gadgets for p = 250 -0.01x dollars apiece, and it…

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Q: Show that the vector field F = is not conservative by showing it is not path independent.

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Q: 2 Iim 3xy + y (39) (0, 0) x² + xy lim (x,y) → (0,0) 2 2 x+ - 4x sxx X + 3x1 + y°

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Q: Find the critical number(s), if there are any, for the function. f(x) = x² - 6x² + 12x + 10.

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Q: A trapezoid has one of its legs perpendicular to both parallel bases. If the altitude of the…

A: According to question,Given,Height of Trapezoid, H = 3 units.

Q: A. Find the Inverse Laplace Transforms of the following functions s+1 1. F(s) S³+2s²-8s =

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Q: Espanol Consider a triangle ABC like the one below. Suppose that B = 100°, a = 7, and C = 24. (The…

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Q: 7. Given a DE: y" + 2y' - 8y = 0 and a solution of the form y = ex for some (unknown) constant "r".…

A: The objective is to solve the above question.

Q: 1. A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined…

A: A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that…

Q: For the parametric equations: = 24et and y = 144e24t (write the number answer only in the box) da dt…

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Q: Find the derivative of f(x) = x tan¯¹(x) + ln(√1 − x²).

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Q: 30. 1 [² ( 1/3 + 1 = 0 + 1 = 10²/3) dw 8

A: Given integral:- ∫0818+12w+13w13dw

Q: (part 1 of 4) Determine fa- fy when 1. 2. 3. 4. 6. f(x, y) = 4x² + 4xy - 4y² + x + 2y. fx-fy = 12x -…

A: Topic = Derivative

Q: find the particular solution (2x+3) sin y dx + (4x^2-9) tan dy = 0 x=0 y=0

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Q: 4. 3 18 D³ - 57 D² - 85D +100= 2

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Q: Use chain rule to find fås for f(x, y) = 2x + 4xy − y² with x = s + 2t and y = t√√s.

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Q: b. g(x, y) c. f (x, y, z) = logx (x) -X₂²

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Q: 6. Use the limit definition of the derivative to find f'(x) if 1 x+2' (a) f(x) =

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Q: The rate of decay of a radioactive material is directly proportional to the amount of the material…

A: Please see the below picture for detailed solution.

Q: Use the Integral Test to determine whether the series shown below converges or diverges. Be sure to…

A: Given, ∑n=1∞5n2+49

Q: marks back yard is 8meters by 4meters . what is the area of the backyard in square feet

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Q: 3xy+у2 lim (x,y)→(0,0) x2+xy

A: To show that the following limit does not exist.limx, y→0, 03xy+y2x2+xy

Q: Evaluate: lim (sin¯¹x)". -1 +0←x 8

A: We have to evaluate the given limit.

Q: 2. Find the general solution of the following differential equation: (x² + 1)y' + 6xy=x a. y=1/3 +…

A: Given differential equation ( x2 + 1 )y' + 6xy = x

Q: Q-5: Using logarithmic differentiation find f'(x) if 4 2x+1 a) f(x) = * √1-3x b) f(x) = xx, x > 0.

A: 5) Given functions, a) fx=2x+11-3x4 b) fx=x1x;x>0

Q: dN dt = 5 - N, N (2) = 2

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Q: 15 CO X…

A: We have to slove above question

Q: Define a function g: Z → N, by g(z) = z² + 1. (a) Prove that g is not one-to-one.

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Q: 6+√2 √3

A: 6+23=6+23×33              =6+233×3              =63+233              =63+2×33

Q: Make a sketch of the region and its bounding curves. Find the area of the region. The region inside…

A: Given query is to make the circle and find the area.

Q: 1) If A is the area of a circle with radius r and the circle expands as time t passes, find dA in…

A: Topic - Application of derivatives We know that Area of circle =A=πr2where r is the radius of a…

Q: (ey + 1)²e-ydx + (ex + 1)³e¯*dy = 0

A: Given differential equation ( ey + 1 )2e-ydx + ( ex + 1 )3e-xdy = 0 ( ey + 1 )2e-ydx = - ( ex + 1…

Q: Find the first partial derivatives of the following: ∙i. f(x, y) = tan(3x − y) + - ii. g(x, y) = xy…

A: To find the first partial derivatives  of the following:i fx, y=tan3x-y+xyii gx, y=xyiii fx, y,…

Q: A. Show that the following limit does not exist. 3xy+y² i. lim (x,y) →(0,0) x²+xy ii. lim (x,y) →…

A: A detailed solution is given below.

Q: Evaluate the following integral, (x² + y² + z²) ds, √(x² + where S is the part of the cylinder x² +…

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Q: 2. A poster is to have an area of 180 in² with 1-inch margins at the bottom and sides and a 2-inch…

A: A poster is to have an area 180 in2 with 1-inch margins at the bottom and sides and a 2-inch margins…

Q: A ladder is leaning against a vertical wall. Due to the smooth ground, the foot of the ladder is…

A: if x is the horizontal distance of the foot of the ladder from the wall and y is the vertical…

Q: If f(x): = 0 * sin(x) S V4 + t2 dt and g(y) = = [ f(x) f(x) dx, find g ¹*(17). 6

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