I. Solve the following problems. af 1. Find af and of the function f(x, y) = arccot (-) + In ( ду -2xy )

Q: au = 6x + 7, du = e*dx. %3D

A: answer is in next step

Q: MyCalStateLA x Activity 10.6 x O Exploring Dir x+ Ohttps://calstatela.instruct... Let f(x, y, z) at…

A: Given query is to find direction derivative.

Q: Given that Vf (5, -4) = 8 i – 7j, find the directional derivative of the function f at the point (5,…

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Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

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Q: alculate V3 + 2i. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 2n.

A: Given query is to find the value of a and b.

Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: An object moves in a straight light according to the position function s(t) = 2te-t where s is in…

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Q: Ans: y' + y2 - y = 0 ae* 5. y= 1+ae*

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 %3D

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Q: Find the volume of the parallelepiped determined by the vectors a = (5, 2, – 1), b = (0, 4, 1), č =…

A: We will find the volume of the parallelepiped by using the given vectors.

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Here, g(3)=4 &amp; g'(x)=x2-16x-2, x≠2

Q: Two angles are complementary.  The measure of one angle is twice the measure of the other.…

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Q: The curve y: 3/2 is rotated about the y – axis. Calculate the surface area for 0<x<2

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Q: Find the directiunal deavative of the function at the given pornt in the direction Lof the rectorv…

A: Given problem:- Find the directional derivative of the function at the given point in the direction…

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

A: Given query is to find the average height

Q: Question A tank is shaped like an upside-down square pyramid, with base of 2 m by 2 m and a height…

A: The volume of square pyramid with side of base a and height h is given by, V=13a2h At any height the…

Q: 7-x 17) dx

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Q: 18. Determine if the equations are exact or not then solve for the general solution. a. (e*(x²y² +…

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Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x2 for -2 sxs…

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Q: 7. Х Arcsec (2х) dx 3 (4x2 – 1)7

A: The objective of the question is evaluate the indefinite integral.

Q: . Prove the following using the epsilon-delta definition of a limit. b. lim x² = 4 X→2

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Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

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Q: Find all the rational zeros of the function f(x) = 2x - 9x4 + 9x³ - 3x² + 7x + 6. -1, 2 x = 을 3,2 x…

A: Roots satisfyf(x)=0f(x)=2x5-9x4+9x3-3x2+7x+6f(-1)=-24f(1)=12Options, A and E ruled…

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic…

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Q: Write the polynomial as the product of linear and quadratic factors that are irreducible over the…

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Q: v = 8i – 5j – 4k - w = -5i + 9j – 4k Compute the dot product v w.

A: The formula for dot product of two vector a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ is given by the…

Q: 9. Evaluate the following definite integrals. S" V5x – 1 dx 10 а. b. J sin 2x dx

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Q: 4. By using Taylor series, show that e* =cosx+i.sin x.

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Q: r = 3 cos 0

A: The given curve,  r=3 cosθ

Q: Simplify f and find any vertical asymptotes of f. x²(x+8) f (x)= x²+ 8x

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Q: Use mathematical induction to prove the given statement for all positive integers n. 20+10+0+..…

A: We have to prove given statement with mathematical induction.

Q: A 20-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

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Q: 1 Using u = 1 + 2x6, then the integral | x°(1+ 2x6)5 dx becomes 12 us du- This evaluates as 5+1 1 12…

A: Follow next step

Q: Find the vector component of v = (4, – 1,7) along b = (2, 6, –9) and the vector component of v…

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Q: Question Determine where the local maxima and minima occur on the graph given. 12 10- 8- -12 -10 -2…

A: From the given graph we can see that there are two local maxima.

Q: Write the form of the partial fraction decomposition of the rational expression. Do not solve for…

A: Reducing to partial fractions

Q: x2 1. Let f(x) = 3Vx² – 1 and g(x) = x4 81 (a) Determine the domain of f and g. (b) Compute gof and…

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Q: Find the fifth term of the geometric sequence from the given information. Express the term as an…

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Q: y=x/x+1 is a solution of what differential equation

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Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = xy. The directional…

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Q: dx Ifz = x + y = -2, dt dy = 3, and z> 0, find dt dz at (x, y) = (4, 0). dt Please give an exact…

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

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: Let s be an acute angle and sin (s) = Find the value of cot () exactly. (Give an exact answer. Use…

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Q: In the following exercises, suppose →1 as n→>∞. Find the radius of a, that convergence for each…

A: We have to find the radius of convergence.

Q: Sa413 - 3x5/2) dx x4/3, 5)

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Q: Write the first five terms of a geometric sequence a} based on the given information about the…

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Q: Let a = ci +jand b 7i + 56j. Find c so that a and b are orthogonal. %3D %D C =

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Q: Find the equation of the tangent line at the given point on the curve. 3y - Vx = 23, (16,3) y =

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Q: 4- 2- 2 3. To find the blue shaded area above, we would calculate: f(z)dz = area Where:

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