1 1 1 Calculate the gradient of h(x, y, z)=33 Vh = h (2xi) + 3yj + 3zk

Q: Problem 6. A particle is moving on a horizontal line. Its distance from the origin at time t20 is…

A: The  particle is moving to the left if the velocity is negative.

Q: Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

A: i) Given:       Fx,y,z=x3i+y3j+z3k then         ∇·F=∂∂xx3+∂∂yy3+∂∂zz3                 =3x2+3y2+3z2…

Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

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Q: Find the absolute maximum and absolute minimum of the function x3 3 f(x) = 1 7x² 2 + 10x - 2 over…

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Q: n = 1 10" 4 +97

A: To determine the convergence or divergence of the given series.∑n=1∞ 10n4+9n

Q: Grain pouring from a chute at the rate of 12 ft3/min forms a conical pile whose height is always…

A: How fast is the height of the pile increasing at the instant when the pile is 8ft high? change in…

Q: TT X S cos dx 2 0

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Q: Use implicit differentiation to find y′ for the equation below and then evaluate y′at the indicated…

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Q: 1. Consider the graph of the function f below. I -4 -3 42 1 5 4 3 2 -1 -2 -5 Y I 1 y = f(x) I I 3 Т…

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Q: Given A [3] find the determinant

A: To find the determinant of given matrix.

Q: to x years is Ix = -0.000354x 3 + 0.00452x²³² + 0.848x²-34.9% + 20,000 age 0≤x≤ 95.2 Find the rate…

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Q: 2. Evaluate = I= √²² + y² + 2² av where E is the region enclosed by the the sphere x² + y² + 2² =z.…

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Q: Let ƒ(x) = x³ – 15x² +27x - 2. Find the open intervals on which f is increasing (decreasing). Then…

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Q: Prove: If U AUB and An B = Ø, then A = U\ B

A: we can prove the  given statement .

Q: 1/2 S 5 sec²(x)tan(x) dx 0

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Q: 3 Given the function of f(x) = -1 + on the interval [-8, -2], find a point c between -8 7x and-2 so…

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Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: To find the exact surface area.

Q: f cos(6x + 5) cos (2x - 7)dx

A: To evaluate the given integral

Q: X Dx f¹2dt 4+t -X

A: We have to differentiate the given equation.

Q: 40. Ten thousand raffle tickets are sold at $2 each for a local library benefit. Prizes are awarded…

A: We need to find expected value.

Q: • [ε (a) Evaluate S (b) Evaluate 3.re dr. r² sin z dr.

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Q: xy Find the linear approximation to f(x, y, z)= at the point (-3,-3,1): f(x, y, z) ~ ←

A: Topic = Derivatives

Q: A bacterial culture grows according to the formula P = Poat. If it takes 9 days for the culture to…

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Q: Suppose that for a company maunfacturing calculators, the cost and revenue equations are given by C…

A: We have to find the rate of change of cost, revenue and profit.

Q: what is math

A: Definition of mathematics

Q: How do you evaluate the following integral: Integral of (-sin2(x)) dx I'm tempted to use the basic…

A: As we know the trigonometric identity: cos2x=1-2sin2x And use the common integral:…

Q: The equation N (t) 550 models the number of people in a town who have heard a rumor 1+49e-0.7t after…

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Q: 1. What does it mean to say that a function is periodic?

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Q: (a) Using algebraic division and integration by substitution, or otherwise, show that - dx = e² −…

A: We can evaluate the given integral by using the substitution u = ex

Q: Suppose that f(5) = 1, f'(5) = 2, g(5) = -7, and g'(5) = 4. Find the following values. (a) (fg)'(5)…

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Q: Find the sum of the first 14 terms of the geometric sequence 1 9,  1 3, 1,   . (Round your answer…

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Q: 73. Which statement determines if set x is a proper subset of set lyl? 1. 2. 3. 4. x.issubset (y)…

A: If there are Two sets X and Y, such that X is a proper subset of Y, it means Y contains all the…

Q: A curve with polar equation 31 7 sin +36 cos 0 represents a line. This line has a Cartesian equation…

A: NOTE: Refresh your page if you can't see any equations. . use the polar to cartesian substitution

Q: Determine the vertex, focus, directrix and axis of symmetry of the parabola with the given equation:…

A: we need to find out the vertex, focus, directrix and axis of symmetry of the parabola and also need…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x.  f(x)= 17e^x…

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Q: Consider two nonnegative numbers x and y where x + y = 14. What is the maximum value of 5x²y? Enter…

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Q: The supply and demand for a product are given by 2p - q = 100 and pq = 300 + 25q, respectively. Find…

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Q: ૨ 2 (D² -2D +10) y =0

A: Solution : Given that DE is

Q: options Yart 1. Find Sin(t) part 2. find cos (t) 10 10 options 8 ㅋ 능 None 10 ㅋ 10 8 3. 10 4.…

A: Topic- unit circle WE are given a point on the unit circle as -810,-610we know that on unit circlex…

Q: ) Obtain the differential equation of the family of plane curve described and sketch at least 5…

A: We have to find the differential equation of the family of plane curves, that is "straight lines…

Q: 2. Convert the following standard a. (y + 1)² = -2(x + 2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. xe3xdx

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Q: 4. Let (n) be an increasing sequence of real numbers. Assume, furthermore, that (x₂) has a…

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Q: Find the derivative (be sure to simplify): f(x) = sinh(ln(x²))

A: Given query is to find the derivative of the expression.

Q: Find the next three numbers in each sequence. Then classify the sequence as linear growth,…

A: Given , two sequences below a) 2,5,10,13,28,21,26,_,_,_ b) 3,6.5,10,13.5,17,20.5,_,_,_ we need to…

Q: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the…

A: Given : A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch,…

Q: At what point (x, y) is the function f(x) = 8x - 3 closest to the point (3, -6)? Enter an exact…

A: To determine the point x, y on the function fx=8x-3 is closest to the point 3, -6.

Q: Assume x and y are functions of t. Evaluate dy/dt for 2xy−2x+4y3=−56​, with the conditions dx/dt=…

A: Given: 2xy−2x+4y3=−56​, dx/dt=-16, x=4 and y=-2

Q: SHOW COMPLETE SOLUTION A right circular cylinder is given. A slice perpendicular to the bases…

A: As we know that Volume of a right circular cylinder is πr2h, where r and h are radius and height of…