Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č = (2, 3, 1). %3D Volume = -21 x cubic-units

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

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A: We have to find following value.

Q: 1. For which function below does lim f(x) = -∞? X-2+ 1 f(x) = - x-2 1 f(x) = - (2 – x) x² - 4 a. с.…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: * Your answer is incorrect. Use Green's Theorem to find the work done by the force field F(x, y) =…

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Q: (b). lim zInz² et

A: To evaluate: limx→0 xlnx2ex Using logarithmic property we can write the given limit as  limx→0…

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A: We need to find cartesian coordinates.

Q: Klara is building a fence in her backyard. The sides of the fence will form a right triangle with…

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Q: 4proof that d sech u = dx - Sech u tanhu.du dx

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = z³ i –x³j+ y° k across the sphere x? +…

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Q: 10. Given the supply and demand functions: P = 10+2Q, P = 30 – Q Which of these statements are…

A: Here the given demand function is             P = 30 — Q Supply function is             P = 10 + Q…

Q: The ellipse shown below has parametric equations x(t) = A cos t, y(t) = B sin t, 0 <t< 27.

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Q: Evaluate using Integration by Parts. (Use symbolic notation and fractions where needed.) хебх+4…

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Q: Comparing Graphs of Derivative Functions Date Given the graph of f(x), sketch an approximate graph…

A: Given graph of function f(x)

Q: dy If dæ 4x³ + 3x? + 6x and y = -3 when x 1, fınd y. |3D

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We have to find the limit

Q: Clairaut's Theorem Let DCR be a disk containing the origin and assume that q : D → R is a function…

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Q: Suppose that f is integrable on [-4, 7]. If the average value of f on the interval [-4,7] is 4.25,…

A: Given: Average value of f(x) on the interval [-4, 7] is 4.25 The formula for average value of f(x)…

Q: Exercise 1 A Write number sentences for the problem situations. Then solve the number sentences to…

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Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x1½ В. — 0.5х-1Vx-1 С. -0.5 1…

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: Q1. Which of these expressions is NOT factorised? А. X(х + 1)(х + 2) В. (х+ 1)(х+2) С. x (х + у) —…

A: Solving the problem by finding the correct answer.

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

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Q: T between -1 and 1, then find a number c in [-1,1] where Find the average value fave of f(r) f(c) =…

A: This question can be solved using the concept of average value of a function in a given interval.

Q: a) Graph the function f(x) = 2x -5x+3 b) Draw a tangent line to the graph at the point whose…

A: Given the function is  f(x) = 2x2-5x+3

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x, x = 1, and y = 0,…

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Q: Evaluate the integral of sec^5 (x) tan^3 (x) dx * 1/7 sec^7 (x) - 1/5 sec^5 (x) + C 1/3 tan*3 (x) +…

A: Given: I=∫sec5xtan3xdx   As we know that; The trigonometric identity; sec2x=tan2x+1 The Power rule;…

Q: -2000x has the marginal-demand function D'x)= where Dx) is the number of units sold at x dollars per…

A: First we'll integrate and the we'll put the given value. So i am providing my handwritten notes…

Q: 9. Use the graph of y = f (x) to answer parts (a) – (f). Where applicable, use interval notation. -2…

A: Solution is given below:

Q: Find the coefficient of w2r?y'z? in (2w-z+3y- 2z+2)°.

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Q: Find the volume of solid generated by revolving the region bounded by the curve y=4/x' and the lines…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: What is the number halfway between 3 - 1/3 and 2 + 5/7 ?

A: Average

Q: Consider the change of variable u = xy and v = 3y + 2x and the integral 2.r + 3y – 6 =0 - ||. (2r²y…

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Q: Find the limit. lim (t i - 5 j+1² k) i+ i j+ i k lim (t i-5 j+r k) = i %3D

A: This question is based on limits.

Q: Graph the function and then find the specified limits. When necessary, state that the limit does not…

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Q: Find the area of the shaded region. y=x-4 y= /2x 2. 8. 10 x -4 2.

A: Given query is to find the area of tha shaded region.

Q: the 1. For f(x) = r8/3 - 4x5/3, find a). the domain and f', b). f" (simplify f"), %3D c). the…

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Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: 3 For the given equation f(x) = x³ +a2 %3D 6x + 10

A: f(x)=x^3+3/2x^2-6x+10 f'(x)=d(x^3+3/2x^2-6x+10)dx f'(x)=3x^2+3/2(2x)-6(1)+0 f'(x)=3x^2+3x-6 take…

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 5

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Q: Yz01003 b00 Cos07+3 2. 7) 300 Sing Y=0.002 Ysine dr do dø

A: A detailed solution is given below

Q: Confirm that the force field F(, y) = 2xy°i + 3x²y°j is conservative in some open connected region…

A: If force field is conservative then it is independent of path.

Q: Find the area of tge region bounded by the loop of y^2 = x(5-x)^2 -about plane area, complete…

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Q: Find the area of the region bounded by the curves x=y3 and y=x2.

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Q: Use a finite approximation to estimate the area under the graph of the given function on the stated…

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Q: Find the work done by the force field F(x, y, z) = xy i+ yzj+xzk on a particle that moves along the…

A: Solution is given below:

Q: b) Find the inflection points. 4. For the given function find the local extrema using the Second…

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