Convert the following product into pi notation.. 10 12 3 11 . 12 . 13 4 14 5 ...

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y-ay-1 and…

A: Given that the solid base is the region in the first quadrant bounded by y=x4,y=1 and y-axis and…

Q: 5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

A: Given, w=f(u, v) where u=x + y and v=x - y To prove: ∂w∂x∂w∂y=∂w∂u2-∂w∂v2

Q: Evaluate the given limit algebraically, if it exists. lim-0 sin 8x 6x-2x³

A: limx→0sin8x6x-2x3

Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

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Q: Give the particular solution of the given intial value problem. Show full solution. xy′+2y =…

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Q: Consider the function. Find f'(x). f'(x) = Find f"(x). f"(x) = Find f"(-1) and f"(4). f"(-1) = f"(4)…

A: The given function fx=x3-3x2+2 We have to find the values of f'x, f''x, f''-1 and f''4

Q: Find direction Vector a that has the same as (-6,5,67 but has length 4

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Q: 1. Evaluate the following definite integrals using the Fundamental The- orem of Calculus (b)+12+ dr

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Q: Divide using long division. State the quotient q(x) and the remainder r(x) 24x to the fourth + 21x…

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Q: Question Determine which of the following tests would be best to use to determine the convergence of…

A: Solution: ∑n=1∞9n37 Apply p series test if the series is of the form  ∑n=1∞1np, where p>0 If…

Q: Question Find the equation of the tangent line to the function f(x) = −3x³ - 2x² 33 x + 3 at the…

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Q: Consider the function f(x)=x³-2-x+2 that has exactly one root. Which of the following intervals…

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Q: Find the vertical and horizontal asymptotes. (Enter your answers as comma-separated lists of equatio…

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Q: Define as the region bounded by the function f(x): and the line x = 1 in the first quadrant between…

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Q: I. The daily temparature high can be modelled by the formula T(t) = 57.5 22.5 cos(2πt) where T is…

A: The daily temperature high can be modelled by the formula                  Tt=57.5-22.5cos2πtwhere T…

Q: Find a polynomial P(x)=x3+ax2+bx+c satisfying ALL of the following properties: i) x = -1 is a local…

A: f(x)=x³ +ax²+bx+c f '(x)=3x² +2ax+b It is given f(x) is maximum at x=−1, hence f'(−1)=0 ⇒f…

Q: Find the first, second and third derivatives of f(x) = 1/x. From this, deduce a pattern and use this…

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Q: Evaluate the integral in terms of the constant: S₁x5 dx =

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Q: Laplace transforms. y' + 9y = 0, y(0) = -1

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Q: A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped…

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 4y and y³ = x with y…

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Q: 6. Consider the surface in R³ defined by x² + y² - 2z² + 6x - 8z = 7. (a) This surface is a quadric…

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Q: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

A: Here we have to use the bisection formula for solving the question.

Q: I dont understand what is written. Can you write in another way or atleast have spaces in between…

A: Here we have to determine the sum of convergent series.

Q: Find the critical point(s) of the function f(x, y) = x¹ +y¹ − 40xy. Enter your answer as an ordered…

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Q: 0 Exercise 7 Limits The following graph of the function f satisfies limf(x) = 2 . For & = 3 find a…

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Q: Give the general solution of the given ODE. Show full solution. y′(2x−3) = 2xy+48x−3y−72

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Q: Differentiate the given function using the appropriate rule(s). Your answer does not have to be.…

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Q: Evaluate the following integrals and state that they diverge or converge.

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Q: Let f(x) ) = be a differentiable function with f'(x) ≥ 5 on the interval [-7, −1]. If ƒ(−1) = −1,…

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Q: For f(x) = 3x² + 8x + 7, find the equation of the tangent line at the following values of x. (a) x =…

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Q: Let S be the solid inside the sphere x2+y2+(z-3)2 = 9 and the below the cone x2+y2 = z2.   Setup…

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Q: Determine all the symmetries of r = 4 sin(1 + cos: 30).

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Q: If g(x) = cos(x) then g'(x) = g'(4) = (round to 3 decimal places)

A: If gx=cosx, then to find g'x and g'4.

Q: Write the integral as a sum of integrals without absolute values and evaluate: ƒ³ |x³| dx : =

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Q: Evaluate the integral. (Use C for the constant of integration.) √(x² + 8x) cos(x) dx (x²sin(x) + 8x…

A: NOTE: Refresh your page if you can't see any equations. . use the integration-by-parts method…

Q: A clown with a spherical head of diameter 25 cm is trying on an oversized conical hat with an angle…

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Q: Calculus Find the standard deviation of the scores: 5.5.5. 8. 11. 11. 11. Round to tenths A) 2.8 B)…

A: To find the standard deviations

Q: Use logarithmic differentiation to find the derivative of the given function. 2 sin a y = x² s

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Q: f(x) = x² - 11x + 30 g(x) = x - 5 (f+g)(x) = (f- g)(x)

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Q: Match the second order linear equations with the Wronskian of (one of) their fundamental solution se…

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Q: Use power reduction formulas to fill in the blanks in the identity below: (sin(3x))¹ = 1 += cos( x)…

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Q: Consider the following system of equations 3 2 7 -2 4-5 1 0 4 x₁ = x = - and the following…

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Q: 22 where x = Finding дх др " 9ret, y = ду дz " др' др " - 2te' & z = ert. дх ду Ət' at & дz at and…

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Q: 4. The marginal profit from making and selling x products per day is P'(x) = 350 + 4x - 3x² Find the…

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Q: Find the critical point(s) of the function f(x, y) = x² + y² − 40xy. Enter your answer as an ordered…

A: To find the critical points of the function fx, y=x4+y4-40xy.

Q: Given 4x - -3x-y-7√ √/5y+ 8z = 5, calculate Provide your answer below: dz dx

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Q: Use a graphing utility to find the limit. 5x − 7 2-81 lim x-g+x².

A: Let's find evaluate the limit by graphing utility.

Q: Divide using long division. State the quotient q(x) and the remainder r(x) 8x cubed - 5x squared +…

A: Solution- Given Dividend=8X3-5X2+9X+2 Divisor = 8X2+3X+5 remainder =? quotient q(x)=?   by Long…

Q: 2. Find lim (√t+3, In(2 — t), ²). t-x

A: Given: limt→∞t+3, ln2-t, 2t