Find div F and curl F of F(x, y,z) = (x z³) i + (3x²y1² )j + (3z?y) k

Q: e or sin 1 2 and tan 2 cos .2

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Q: Find all critical points of the function f(t) = t – 4/t + 1. (Use symbolic notation and fractions…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: Consider the function f(x) = x2 -1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: Which of the following statements is true for the function f whose derivative is f'(x) = (x + 2)e-*…

A: Here we have to find the intervals where the function is increasing and decreasing.

Q: Suppose that f is defined everywhere and x = 2 and x = -1 are the only critical numbers for f. If f"…

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Q: Find all critical points of the function f(x) = sin-'(x) – 8x for –1 < x < 1. (Use symbolic notation…

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Q: Compute the given integral. fain' sin" x cos xdx +C

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Q: Hiw:-boundary Value problems- Q/solve xy-ý=o yco)+ ylo)= 1

A: We have to solve the differential equation.

Q: What are intervals of concavity of the function f(x) = -2x' + 6x² – 3 ? O a. Concave upward on (1,…

A: Given query is to find the the interval where function is concave upward and downward.

Q: èrentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2).

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Q: QUESTION 15 Not yet answe Find the domain and the vertical asymptotes, if any, of the following…

A: We have to find out the domain and asymptote

Q: 2. Express the shaded area of the region shown below by double integrals of order of integration (1)…

A: The shaded region's area is: The difference between the area of the complete polygon and the area of…

Q: 3a-6 Differentiate y= csc =CSC 5z2+9 A g' = cot() cse () ( ) B. y' = - cot() csc() ( ) 3x-6 522+9…

A: Given: y=csc3x-65x2+9 As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Chain rule:…

Q: answer

A: We will find the second derivative.

Q: Se*(4 + e*) dx Evaluate the integral of A (4 + e*)² + c B. (4 + e*)? +c (4 + e*)² + c (4 + e*)* + d…

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

Q: Eliminate the arbitrary constants on the given equation: y = Ae + Bxe" O y = y' – 2y O y' + 2y +y =…

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Q: e3 1 - Find lim

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

Q: - If v1, v2 are 2 vectors in a vector space V such that 0 = 4v1 – 2vz. Then{v1, v2 } are linearly…

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Q: 1 (tan x + cot х) sec x %D 1/cosx 1/sinx 1

A: Given query is to find the correct option for the expression.

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Express the vector 2u + 5w in the form v = v,i+v2j+ V3k if u = (4, - 5, 2) and w= (-3, 2, - 4). 2u +…

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Q: -2 is a critical number of the function f(x) = V2x - x². Select one: True O False

A: We can solve this as follows:

Q: 8 In what quadrant does the angle lie? 7pi/3 IV II I III

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Q: The rectangular coordinates of a point are given. Plot the point. (-4/z, -4/2) y y 5 5 X -5 -5 -5 -5…

A: Here we will find the correct option and two sets ,

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: he region between the graph of y = 4x – 8 and the x-axis from - 2sxs6 Ay 30-

A: Topic:- geometry

Q: If 2n+3 a %3D 5n+8

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Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: 1. rate at two-hour time intervals are shown in the table. Find lower and upper estimates for the…

A: Given:      The lower and upper estimates for the total amount that leaked may be computed as the…

Q: Q: Solve the following D.Eqs. (Use undetermined coefficient method) 1) y" – 2y' + y = xe* 2) y(4) –…

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Q: Evaluate, with an exact value, the definite integral º -1/1+a dx.

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Q: 3. V4- (x – 3)²dx.

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Q: 2 Find the definite integral fo5 tan(x)dx using strips of width for the trapezium rule correct to…

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Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

Q: Express the following vector in the form v = v,i+v2j+V3k. 3u - v if u = (4,6, – 8) and v = (2, –…

A: We can find the answer as below.

Q: Find the definite integral o tan(x)dr using strips of width for the trapezium rule correct to three…

A: Trapezoid rule

Q: Identify the curve. x 2 + y 2 = 1 parabola circle point circle hyperbola ellipse

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Q: (b) Lines of reflection Lines of reflection Lines of reflection Order of rotational symmetry Order…

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Q: For the points P1 (4,8,7) and P2(5,7,6), find the direction of P,P2 and the midpoint of line segment…

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Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by variation of parameters…

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Q: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.

Q: Consider the function f(x) = x* + 2x. %3D

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Q: Find the distance between points P, and P2. P,(4,5,2), P2(6,2,8) The distance is (Simplify your…

A: The distance between two points P and Q is given by: d(P1,P2)=(4-6)2+(5-2)2+(2-8)2

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

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Q: A quadratic polynomial y = 4x +7x-3 has roots pand q. Find a quadratic g(x) +ar+B with roots r= and…

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Q: Give an example of a differential equation  and  classify according to   order, degree ,linearity…

A: answer is in next step

Q: if f(x)=(5+x4)1/4 what is (f(x))2

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Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: A car travels down a highway at 50 m/s. An observer stands 250 m from the highway. (a) How fast is…

A: Topic:- application of derivatives