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Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: 9. 87 12 5 -

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Q: the answer is incorrect

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Q: Q14 Find the equation of the tangent line to the curve f(x) = 2x²(x − 3) at x = 1.

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Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: - 49 -dx = X (Type an expression using x as the variable.)

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Q: Find the volume of the region bounded above by the paraboloid z = 4x² + y² and below by the square…

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Q: For a certain mammal, researchers have determined that the mesiodistal crown length of deciduous…

A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

Q: The region bounded by f(x) = −1x² + 6x + 27, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: A function y=f(x) is said to be increasing in the interval (a,b) if for every x∈(a,b), f'(x)>0.…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: We need to change the integral into polar integral ∫0ln6∫0ln62-y2ex2+y2dxdy

Q: Find the derivate of the function: a) f(t) = ₁ (t²-a) 8 F'(() = b) f(x) = 7 (x²³ - 7 x² + 4) 2 f'(x)…

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Q: sin 5 (17x) dx = [

A: To evaluate : ∫sin517xdx Let I = ∫sin517xdx ⇒I =∫sin417xsin(17x) dx

Q: f(x,y)=200(y + 2) represents the "population density" of a planar region on Earth, where x and y are…

A: Given: The population density is f(x,y)=200(y+2) Where x and y are in miles.   Curves are given as…

Q: The sum of integrals below give the area of a region in the xy-plane. Sketch the region, label each…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. y² + 8y +49 (y² +49)²…

A: The given integral is:∫y2+8y+49y2+492 dy

Q: The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. "It is a good thing…

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Q: A volume is described as follows: 1. the base is the region bounded by y = 9 - 1x² and y = 0 2.…

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Q: A ball of radius 15 has a round hole of radius 9 drilled through its center. Find the volume of the…

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Q: . In the Gizmo, select sine wave so the parent function is f(x) = sin (x). A. The sine wave is a…

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Q: Find the derivative of the function. In(e²x + 3) y =

A: y=lne2x+3d dx(lnx)=1xd dx(ex)=ex

Q: Consider the function f(x) Enter an antiderivative of f(x). Do not enter +c as part of your answer.…

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Q: Each of the limits below represent a piece of the passcode that you must enter to proceed. The…

A: We have to find the limits to get the passcode.

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Find the volume of a pyramid with height 29 and rectangular base with dimensions 3 and 8 using…

A: Let h be the height of the pyramid, and l and w be the length and width of the pyramid. Note that,…

Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy dx = 0 =

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: If x=c is a critical point of the function f(x) if f(c) exists and if either f'(c) =0 or f'(c) does…

Q: 5 The curve y = -5 x³ + x² + x + 1 "Trident of Newton". y 7 1 X 1 y= is known as the x³ + x² + x + 1…

A: To find the coordinates of the point where tangent to curve is parallel to y=2x.

Q: The number of hits on a certain website​ (in thousands) is approximated by f(x)=30e^0.171x​, where…

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Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 Find the differential dy when x…

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Q: Find the surface area of revolution about the x-axis of y = 5 5 ㅠ 0 ≤ x ≤ 5 sin(5x) sin(5x) ov over…

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Q: TOPIC 4-5: L'Hôpital's Rule x²-25 x+∞5-4x-x² Q. #11 Please evaluate Lim a) Using L'Hôpital's Rule as…

A: L’hospital rule  limx— a f(x)/g(x)   = limx— a f’(x)/g’(x)   now find limit

Q: Consider the function f(x) = 12x³ +30x¹ - 160x³ +4. f(x) has inflection points at (reading from left…

A: Application of Derivative

Q: - Find the inflection points of f(x) = 2x¹ + 10r³ — 18r² + 7. (Give your answers as a comma…

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Q: A volume is described as follows: 4 x² and y = 0 25 1. the base is the region bounded by y = 4- 2.…

A: Given the base region is bounded by y=4-425x2 and y=0. ymax=4-425x2max=4 From y=4-425x2 ,x = ±524-y…

Q: Find the derivate of the functions: a) F(x) = -3x²=4 : f'(x) = b) g(v) = 3 g'(v) = 2√² +5V-9 c) f(x)…

A: We need to find out the derivatives of the given functions.

Q: Find parametric equations of the line that contains the point P(3, 1,-2) and intersects the line L:…

A: The solution is shown below-

Q: x² 2 ,0sxs Find the length of the curve y=- 3√5 2

A: To find the length of the curve y=x22, 0≤x≤352.

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: Given the points A: (-6,-4,2) and B: (3,-2,0), find the vector u = AB

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Q: Let a = (3, 5, — 3) and b = (1,3,0). Find the projection of b onto a. proja b=

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Q: Find the arclength of y = 2x² - 5 on 0 ≤ x ≤ 1

A: Given: y=2x2-5 on 0≤x≤1 To find: Arc length.

Q: After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's…

A: Given f( x ) = ( x4 - 2x ) g( x ) = ( x2 + 2x - 62 ) h( x ) = 2x - 13

Q: Differentiate the function. f'(x) = f(x) = log₁0(x⁹ + 7)

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Q: The equation of motion of a particle is s = t³ - 12t, where s is measured in meters and it is in…

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Q: (a) Use differentiation to find a power series representation for 1 (6 + x)2 f(x) = f(x): 00 Σ n = 0…

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: To find out the critical points, increasing and decreasing intervals and also the extrema and at…

Q: If 3 A = -4 -4 8 1 x 4 1 1 Is a singular matrix, then x is 1

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Q: P'(W): = P(w) = 6w² - 2w + 4 VW

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Q: Evaluate lim x→∞ _x3 _ 5x2 +52 – 2 x² + 4x +3 =

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