Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w is |u. (vx w)| to determine the volume of W 6 P(-2, 3, 0), Q(2, 1, −3), R(1,0,1) and the tetrahedron with vertices S(3, -2, 3). NOTE: Enter the exact answer. V =

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: Find the curvature K of the curve given below. r(t) = ti+8t²j+2tk

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Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

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Q: Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the…

A: Given that      36x2y''+24x2y'+8y=0…

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A: Given, ∫tan2(x)sec4(x)dx

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Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

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Q: Find lim f(x) if I-00 4x - 1 I 5.

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Question 12 a)! Let C be a curve defined by the vector equation r(t)=. P(32, 52, e³2) Show that the…

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Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

A: This question can be solved using the concept of derivatives.

Q: Integrate | VE 1-4x² dx using a trigonometric substitution.

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Q: x(t) = L−¹ x(t) = L−¹. x(t) = L−1 .2 S² + 5 (3s² +9) (7s² - 5s +6) s² (s + 2) -4s² - 4s - 4 (s +…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Consider the following. w = √36 - 2x² - 2y², x = r cos(8), y = rsin(0) (a) Find aw/or and aw/00 by…

A: We can solve this as follows:

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y = r sin(8), and note that (x,…

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Q: Find the points of inflection of the graph of the function. (Round your answers to three decimal…

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Q: Find all values of x and y such that fx(x, y) = 0 and f(x, y) = 0 simultaneously. f(x,y) = 2x³ 14xy…

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Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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Q: Prove the identity. 2 sin 20 cos 20+ cos 40=1-sin 40 To verify the identity, work each side…

A: sin2θ+cos2θ = 1.

Q: (a) √ (e² +2²) dz (b) f 3² dr

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Q: Work problem 1 Consider the ellipsoid given by the equation: .8 53 - 5z². X + y 4 8 a) i ]Find the…

A: Let's find equation of tangent plane and normal line.

Q: lim X-00 X *3)* X 1 1+

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-1)^-1_57 47n3 n = 1…

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Q: Solve the following initial value problem: with y(1) = 4. Put the problem in standard form. Then…

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Q: Use a graphing calculator to determine which expression can be used to complete the identity below.…

A: topic- trigonometric identities identities useda3+b3=(a+b)(a2+b2-ab)sin2x+cos2x=1

Q: (2xy4e + 2xy³ + y)dx + (x²y4ev - x²y²-3x)dy = 0

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Q: Calculate the sum of the series Σ n = 5-6(0.6)" 00 n = 1 n whose partial sums are given.

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Q: the region enclosed by y = e¹¹, y = 5², and a e = 1. Find the area of the region.

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Q: Answer the following True or False. 4ª + C In 4 faº f₁² da = True Faise

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Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

A: Given problem:-

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given problem:-

Q: F8 e³ti+cos(5t)j +3sin(5t)k 3 -i+cos(5t)j +3sin(5t)k Question 7 The position vector r(t) =…

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Q: The rate of change of N is inversely proportional to CSC(x) · N(x), where If N () = 1, and N (5) =…

A: Given: dNdx∝1cscx.N

Q: u⃗=5i⃗−j⃗− k; v⃗=−i⃗+5j⃗+8k.  Find the projection of u ⃗ onto v :⃗

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Q: Let f(x) = x² - 5x. (A) Find the slope of the secant line joining (3, ƒ(3)) and (9, ƒ(9)). Slope of…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: Solve, finding all solutions in [0,2x) or [0°,360°). 2 sin‘x+ sinx=0 2

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Q: 2. Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature…

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Q: Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=36-x². Graph the…

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Q: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

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Q: ex-4e-x ex 2 x-² / + C ex Option 1 dx 2 x + ² + C ex O Option 3 x+2 ex + C O Option 2 x-2e * +C O…

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Q: Find all values of x and y such that fx(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 5xy…

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Q: What is the area of the region between y=x²-2x-3 and the x-axis from to 6? x=0

A: Area bounded by the curve fx=x2-2x-3 and x-axis on interval 0, 6

Q: 1. Describe what it means for a relation to be a function. Provide an example of a function, and…

A: Description given below with example

Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

A: We have to find the work W required to pump the water out of the spout.

Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: Find both first partial derivatives. = In ( + ) əz əx əz ду || = Z (No Response) (No Response)

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Q: Find and simplify the function values. f(x, y, z)=√x+y+z

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