1. List and classify all the critical points of the function f (x, y) = (3x^2)y − 6x^2 − 12y^2 + 2

Q: Let r(t) =< √√t4 – 5, cos (t−5), te¯t Find ¹(t) 7¹ (t) = <

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: Given a cone of diameter x and altitude of h. What percent is the volume of the largest cylinder…

A: given:-  cone diameter = x altitude = h. to find:- % volume of maximum volume of cylinder inscribed…

Q: i and ĵ are unit vectors. An angle of 20° exists between vectors ū and where u = 3î and v = 5ĵ.…

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Q: Given y' = cos² x sin y and y (π) = 4, what is y?

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Q: A box with a square base and open top must have a volume of 48668 cm³. We wish to find the…

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Q: T* - sin(4x) lim x 12 x² - 6x +3

A: The given limit is limx→12πx-sin4xx2-6x+3. We have to find the given limit.

Q: Find the derivative of x4 12 1. f'(x) 2. f'(x) 3. f'(x) 4. f'(x) 5. f'(x) 6. f'(x) f(x) = = = x8 +1…

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Q: .  Set up an integral for the area of the shaded region. B. Evaluate the Integral to find the area.

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Q: TUTTIME KETE DE T 15 615 00 AD JIZ IT EIX LIR NON UL what is the slope at points A, B, and C…

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Q: Solve -x3 = 3x to 2 decimal places. S solution

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Q: When a ball is thrown vertically upward the moon with a velocity of 15 ft/sec its eight, y(t), in…

A: Given data

Q: R3 = Then improve your estimate by using six rectangles. 6 = Sketch the curve and the approximating…

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Q: Use the given transformation to evaluate the integral. SSS x²y² dx dy dz, x = 7u, y = 8v, z = 5w R…

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Q: Find the gradient vector field of f(x, y) = x²y³ A

A: The gradient vector for the function f(x, y) is: ∂f∂x, ∂f∂y

Q: Find the gradient vector field of f(x, y, z) = 5x+10y+11z

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Q: Find the magnitude of v. v = (-8, -2, -4)

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Q: Question 2 The closed interval [a,b] is partitioned into n equal sub intervals, each of width Ax, by…

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Q: = [ (2³) 26¹ +4 dx Evaluate = +C

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Q: Given that:  f(x)= x7h(x) h(-1)=3 h'(-1)=6 Calculate f'(-1):

A: Given;

Q: Find all values of r at which the function x-8 f(x) = x² - 6x +8 is not continuous.

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Q: Use the transformation u = x + y, v=y-x to evaluate the given integral by first writing it as an…

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Q: The graph shown is f(x) = 2x². What is the integral that defines the area under this line between x…

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Q: 12 = f(x,y) fl X=r²²+5² y=zr³ 2 find 3²2 aras

A: z=f(x,y) x=r2+s2 y=2rs.

Q: Find a vector-valued function whose graph is the plane x+y+z== a. r(u,v)=ui-vj-(3-u-v)k b. r(u,v)=…

A: The equation of plane x+y+z=3

Q: K Find or approximate all points at which the given function equals its average value on the given…

A: f(x)=-(π/4)sinx  on interval [-π,0]

Q: 11. Practice similar Help me with this Given the geometric sequence: 27, 6.75, 1.6875,... Find an…

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Q: Evaluate S F · dỡ where F = (z, 4y, 2x), and C is given by r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ ñ o

A: F→=z,4y,2x and C is given by r→t=t,sint,cost

Q: Find (a) the general solution and (b) the particular solution for the given initial condition. 8 y'…

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Q: Find the slope of xy = 8 at the point (2,2). A. 2 B. -1 C. -1/2 D. -2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x…

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Q: it says to write you answer to 2 decimal places

A: Giuven that log4(3x-11)=2

Q: yy and y y. your answer, nswer with the positive expression. For example, if y = ±√√x+2, answer with…

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Q: F(x, y, z) = (z, y, x), E is the solid ball x² + y² + z² ≤ 81

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Q: Use the intermediate value theorem to show that the polynomial function has a zero in the given…

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Q: Evaluate the iterated integral. ITT* 12 7ze-x7 dy dx dz

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = xe¹² |

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Q: Find the curvature of the curve (t) = (5 cos(2t), 5 sin(2t), 2t) at the point t = 0 Give your answer…

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Q: The function f(x) = ln(1 − x²) is represented as a power series f(x) = Σno Chan. in=0

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Q: 16. f(x) = x², -1<x<2

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Q: Suppose J is a continuous function, and we know the following data: t 7.5 8 8.5 9 9.5 10 10.5 11 4.3…

A: △x=b-an=11-74=1   For left Riemann sum =△x(f(7)+f(8)+f(9)+f(10))   Therefore to calculate left…

Q: A certain function f is known to have the properties lim f(x) = 2, 118 Determine if I lim x-0- lim…

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Q: c) Solve for x the equation In(x² + x) =ln (15-x²).

A: given,  lnx2+x=ln15-x2

Q: Solve the equation log4(3x - 11) = 2. Write your answer to two decimal places.

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Q: |A curve is given by r(t) = (4t²,e¹, Int). Find a parametrization of the tangent line when t=1.

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Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:…

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Q: Find the absolute maximum and absolute minimum values of ? on the given interval.

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Q: An oil company has a cylindrical drum with a capacity of 645 cubic yards. To construct this drum,…

A: Given Capacity of cylinder= 645 cubic yards. Cost of materials for the top drum is $13 per square…

Q: Describe the graph of the equation. r =(5-2)i +8rj O It is a line in 2-space through the point (5,0)…

A: r = (5-2t)i +8tj

Q: Food and clothing are shipped to victims of a natural disaster. Each carton of box of food weighs 50…

A: Let, x be the number of food cartoons and y be the number of clothing cartoons. Then maximize…