QUESTION 2 In the figure below a = (3,1,0) and b= (2,5,0) X Z B TO If 0 = π, what are both a b and a × b ?

Q: Evaluate the following improper integral. If the integral is divergent, enter "divergent" as answer.…

A: As we know the Power rule: ∫xndx=xn+1n+1+C   The given integral is: I=∫01x1-x23dx   ...1

Q: 9) Solve the triangle that has sides 4 ft, 5 ft, and 8 ft. Draw a picture of the triangle with the…

A: Let's solve triangle all angles.

Q: Determine whether each statement is true or false. You have one submission for each statement. (a)…

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Q: You deposit $1550 in a savings account paying 3.7% simple interest. How much interest will you earn…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = y cos(x - y),…

A: Given z=y cos(x-y)      ; (4,4,4)

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: A bacteria culture initially contains 300 cells and grows at a rate proportional to its size. After…

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Q: 2. A carpenter has a 10 foot long board to mark off a triangular area on the floor in the corner of…

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Q: Find the following using the table below. X f(x) f'(x) 1 2 3 4 +3+ 4 g(x) 2 g'(x) 4 1 2 -~-~ -33 1 2…

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Q: L'Hôpital's Rule does not help with the following limit. The expression keeps on cycling. Find the…

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Q: Find the slope of the curve at the given point. 8y +7x5=5y + 10x at (1,1) The slope of the curve 8y…

A: I am attaching image so that you understand each and every step.

Q: Find the general solution of the following differential equations:- 1) x² (y² + 1)dx + y√x³ + 1 dy =…

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Q: 5x + y ≤ 10 x+y≤6 x≥0, y≥0 Ing system. 100 8 4

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Q: [5/4 sin x dy dx

A: Here we have to find the double integral.

Q: Which of the following functions is not differentiable on all of its domain? Select one alternative:…

A: Given options:- a) x2+1 b)x+1ex c)x2-1 d)lnx2+1

Q: Find the values of A and B such that the graph of the exponential function f(t) = AeBt goes through…

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Q: You are a lifeguard and spot a drowning child 40 meters along the shore and 50 meters from the shore…

A: Distance along the shore= 40m Distance from the shore= 50m Run speed = 4 m/sec  Swim speed = 0.9…

Q: 7. Compute fa, fy, and fz. (a) (x² + y² +22)-1/2 Straight forward (b) sin-¹(xyz) Straight forward…

A: Please see the below picture for detailed solution.

Q: If f(x) = √7x, find f'(x). Find f'(2).

A: Solve

Q: Let g(x) 10x + 12 3x + 6 Find the derivative of g'(x). g'(x) =

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Q: y= у ха т x-1

A: We know, log(a/b)=log(a)-log(b) log(x)=1/x

Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

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Q: e² 82. · [ (v + In u) dv du e In u

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Q: Find the exact length of the curve. y 1/4x² - 11/12 In(x), = -X 1 ≤ x ≤ 4

A: We will find the curve length as shown below

Q: Set up but nit evaluate an integral for the area of the surface obtaining by rotating the curve y=…

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Q: Find the general solution of the given differential equation: Oy Inic(1+x) = 1 Oy Injc(1-x) = 1 O…

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Q: Convert the equation from polar to Cartesian r²sec² +4rcos-r² tan² = 0 a) b) r = 3 sint cost

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Q: What is f'(x) if f(x) = -? 40x5 ex

A: Given data, fx=40x5ex

Q: Using calculus, find the equation of the tangent line to the function f(x) = 3 cos x when = 2.2. The…

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Q: Which of the following is a normal vector to the plane which is parallel to vectors (0, -3, 1) and…

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Q: Solve for the particular solution of the given IVP: O (t^2+y^2)^1.5 - 3ty = 89 O (t^2+y^2)^3 - 3ty =…

A: The given initial value problem is: dydt+y-tt2+y2t-yt2+y2=0 ;       y(4)=3

Q: Given the function f(x) = = 9x³101x² + 274x - 56, and knowing one factor is (9x - 2), write f(x) as…

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Q: An open-top box is to be made from a 32 in. by 22 in. piece of cardboard by removing a square from…

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Q: In Exercises 1-17 find a particular solution. y' + 3y + 2y = 7 cos x - sin x y" + 3y + y = (2-6x)…

A: Note: - According to the company policy we can attempt only one question so please upload the next…

Q: Find an equation of the tangent plane to the given surface at the specified point. Z = = 4(x - 1)² +…

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Q: interval. f(x) = x³ - 6x² + 9x + 22, on [-1,2] 3. Find the absolute extreme values of the function…

A: Given: fx=x3-6x2+9x+22, on -1,2   Use the Power law: ddxxn=nxn-1 For maximum and minimum values…

Q: 0 Find the sum of the series > k=1 (a) (c) 12710 2 (b) (d) 3 (ⅱ). 3 5 11 10

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Q: 10. Find the Taylor polynomial P4 for f(x) = In x at xo = 1. (a)_1+ ²(x-1)=(x-1)² + ²/(x-1) - 1 4 5…

A: Given f(x)=ln x    x0= 1we want to find taylor polynomial P4(x)

Q: Question: t²y" - 2ty' + 2y = 4t², t> 0; y₁(t) = t. Please help me solve this using variation of…

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Q: find the second derivative of the function

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Q: Set up, but do not evaluate, an integral for the length of the curve. ST 2 x = 4 sin(y), Osys (C dy

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Q: Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's…

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Q: Solve for the general solution: Oy 0.25x^2 sin(4x) + cx^2 Oy -0.25x^2 sin(4x) + cx^2 Oy -0.5x^2…

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Q: 9) Solve the triangle that has sides 4 ft, 5 ft, and 8 ft. Draw a picture of the triangle with the…

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Q: Problem 3. indeterminate form. Follow the directions to find the limits in non-standard -x (a) lim…

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Q: If f(x) x+1 4x 3x + 5 13x + 5 3x + 3 13x + 1 3x + 2 and g(x) = 3x x + 3' then (gof)(x) is

A: given  f(x)=x+14x                        g(x)=3xx+3           gof(x)=g(f(x))

Q: 12. A bank account grows at 5% interest compounded semiannually. How long will it take for the…

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Q: Find the local quadratic approximation of f(x) = x³ to find the approximation of 1.03³ at xo = 1,…

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Q: 3) Find all the solutions to 3(1 − cos 0) = 1- cos² 0.

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Q: 8) Prove sin (x+y) sin (x-y) = tan(x)+tan (y) tan(x)-tan (y)

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