Find the point on the curve y = (x − 8)² +9 at which the curvature K is a maximum.

Q: If f(x) dx = 3 and g(x)dx = −2, then which of the following must be true? I. f(x) > g(x) for all a ≤…

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Q: The area enclosed by the two curves y = x² - 4 and y = x - 4 is given by. a. f(x-x²) dx b. (x²-x) dx…

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Q: The vectors A = 3i+j+4k,B=2i-3j-k, find vector normal to A and In plane of A and, B.

A: To find the Normal vector to A & B.

Q: Find and sketch the domain of the function. f(x, y) = √√√√4x²-√√25-y² O -6 DO -4 -6F 4 6 -6 -4 4 4…

A: The set of points (x, y) where the function f(x, y) is called the domain of f(x,y).

Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: solve

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: Draw a graph to match the description given. f(x) has a positive derivative over (-∞, -1) and…

A: Here, given that the function f(x) has a positive derivative over -∞,-1 & (-1,7) and a negative…

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

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Q: Find the producers' surplus at a price level of p = $56 for the price-supply equation below. p=…

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Q: Find the solution of the initial value problem y" — 2y' – 3y = 6te²t, y(0) = 1, y′(0) = 0. NOTE:…

A: We have to solve the given differential equation.

Q: 3. y" + y = sin x

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Q: (a) Assume that f(x, y, z) and F(x, y, z) are arbitrary differentiable functions such that f(x, y,…

A: Given

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: a dy Find given y = 4 In da

A: The given function,   y=4x lnx

Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: Solve the differential equation: dx dy + x = e-y.sec²y

A: Here we have to solve the differential equation.

Q: SSF-n de of F-xy 1-2 k outward (normal away from the z-axis) through the cone z-6√ Use a…

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Q: Consider the graphic representation of f 1 -3 According to the graph, which option is true? (Existe…

A: limit

Q: In the year 2000, the population of a small city was 48,000. The population grows at a rate of r(t)…

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Q: Find an equation of the tangent line to the graph of y = x³ 3x - 1 at the point (2, 1). - 09x+y+17 =…

A: We can solve this as follows:

Q: Find given that x = sec² y. dy dx Osec² ytan y cos² ytan y Osin² y cot y Ocos² y cot y

A: We know that derivatives power rule is  d(xn)/dx = nxn-1.     Here i attached the solution of this…

Q: ubscription. a. Based on the graph of J, hind the root of the equation 6x³ 19x2 + 16x-4 = 0 that is…

A: We need to find root.

Q: -4 -3 -2 -1 0 3 4 1 2 Write an interval to describe the set of values shown above.

A:

Q: I Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: Given that Line is passes through A(1,2,3) and B(5,1,7) And plane passes through C(1,0,2) D(5,1,6)…

Q: We must integrate y = (8x-x2)-(2x) = 6x-x². The limits on the integral correspond to the smallest…

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Q: y = 2 sin(x), y = ex, x = 0, X = K|N 2

A: The region bounded by the curves,  y=2 sin(x), y=ex, x=0, x=π2

Q: Evaluate the integral. 11 sec 40 tan ²0 do 11 sec 40 tan ²0 d0 =

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Q: dy -(x²+y) B)Solve differential equation = dx x+siny

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(8r - s, s² - 7r). Use the table…

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Q: Given that f(x) = (x - 6)² and g(x) = 1 and g(x) = 1 – 2x, find

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Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: B)Is w = Zez analytical function or not?

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: Question 9 Given f(x, y, z) = zey 0 0 01- 02-/ O 2e² - 3 Onone of the choices - X sin (#), what is…

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Q: If y, and y, are linearly independent solutions of t²y" + 2y' + (5 + t)y = 0 and if W(y₁, y₂)(1) =…

A: Given

Q: Assume that f is continuous on the set of real numbers. Find a and b given that cb 3 f(a)da - [³…

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Q: S 2³x dx = 0 23x+1 3x+1 23x In 2 O O O + C + C 23x + C In 8 2³x In 2 + C

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Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: Q4A) Find area bounded by y = 0, y = √x-x² using double integration.

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Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: Find y': ○ 4kx (2kx + 1)7 ○ 4k (2kx + 1)7 ○ 8k(kx² + 1)7 ○ 8kx(kx² + 1)7 y = 1/(kx² + 1)8 ; k…

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Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: you are driving a car away from home.your velocity t hours after noon is given by,…

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: Q3A)Find normal line and parallel plane to the function f(x, y, z) = x²y³z² - 4 At point (1,-1,2).

A: Given function f(x,y,z)=x2y2z2-4

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Find the area of the shaded region. y y=8x-r 15 (6, 12) 10 A y=2x 2 4 6 Step 1 To find the area…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Given, f(x) =(2x-3) g(x) = -4x2+9 = 9-4x2 = (3)2-(2x)2 = (3-2x)(3+2x)  h(x) = 4x2-12x+9 =…

Q: The graph of the function 86 f(x) can be obtained from the graph of y = f(x) by one of the following…

A: Solved below.

Q: Use the properties of the derivative to find r(t) = 3/i+6f³j+31³k u(t)=2i+2r²j-3t³k [r(t) - u(t)]…

A: This question is related to derivative, we will solve it using given information.