D₂ tan³ x = 3 sec O 3 tan² z O secr O 3 tan² z sec²

Q: A tank contains 80 gallons (gal) of pure water. A brine solution with 2lb/gal of salt enters at 2…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: For the function f(x) = 3x − 5 ln x determine a) Domain of f, b) Critical points of f, c) Intervals…

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Q: 11. Describe as many equivalent conditions as possible for a given vector field F is a conservative…

A: Given : F→ is conservative.

Q: Find the value of y at the point on the ellipse x² + y² = 1 16 where the maximum of the function…

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Q: Find te dx

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Q: Solve the following system of equations using an inverse matrix. You must also indicate the inverse…

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Q: defined on the interval [-9.4247778, 1.45619445]. Enter points, such as inflection points in…

A: Solution: Given f(x) = sin2(x/3)       interval [-9.4247778 , 1.45619445]

Q: Find given that cot (3x-2y)=2x-3y. dy da

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Q: If y = (1+x)8 (x + 1)7 True False then dy dr

A: We can solve this as follows:

Q: Problem 3. Evaluate each limit. If the limit is infinite, state whether it is -∞ or +∞. If the limit…

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Q: A plane Π2 intersects Π1: 4x − 2y + 7z − 3 = 0 at right angles. Two points lie on Π2: A (3, 2, 0)…

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Q: x³-7x² +10x x²+x-6 4. lim: x-2 5. lim sin лw w4 w²2²-16

A: The objective of the question is determine the indeterminate form of given limits.

Q: Suppose an object moves along the y axis so that its location is y = f(x)=x² + x at time x (y is in…

A: If position vector of an object is given by  y=f(x) then(i)     Average rate of velocity…

Q: 2. y (0) = Find the solution to the differential equation below satisfying the condition -2. x…

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Q: For second-order differential equations that cannot be solved by algebraic methods, the…

A: For second order differential equations that cannot be solved be algebraic methods, the leibniz -…

Q: A person x inches tall has a pulse rate of y beats per minute, as given approximately by -1/2 y=598x…

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Q: 20- 18 16- 14- 12 10 Co 8 6 4 2 1 Estimate the instantaneous rate of change at x = 1

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Q: Given the following equation: y=2x - 3 " y = -3 y = 3 3. Which is the correct graph of the following…

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Q: Find the indicated derivative. f'(-5) = If f(x) = x², find f'(-5). X

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Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: 9-x² - y² SS. 0 9-x² 0 √√x² + y² dz dy dx 2

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Q: Choose the correct statement given that fő f(x) dx = 7 and f(x) dx = -1 A. f f(x) dx = 8 C. f f(x)…

A: Above question is solved.

Q: 3. Find the volume of the solid that results when the region enclosed by the curves x = = y² and x =…

A: If the region bounded by x=f(y) and x=g(y) on [ a, b], where f(y)≥g(y)is rotated about the y‐axis,…

Q: Find the area of the region enclosed by the following functions.

A: The given two curves:y=x3-3x+3 and y=3x2-2x.We need to find the area enclosed by the curves.

Q: Determine whether the series converges. O The series diverges. O The series converges. Σ k In(k + 4)

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Q: 8. How many terms are in the expansion of (2x - y)¹⁰? A. 9 B. 10 C. 11 D. 12

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Q: lim x-1 2x³ +3 3x² + 1 - 3x + 2

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Q: Evaluate 3 J (nay) dv 11. Gr kabriod if G. is the solid bounded by the parabolic cylinder 2=7³3 J my…

A: We need to find volume.

Q: What is the equation of the line tangent to the graph of y = 2x³/2 at the origin? Oy=0 Oy = 2r Oy =…

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Q: Question 8 At what numbers is the function f(x) = Sommer O At all real numbers O At all real numbers…

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Q: The graph shows the function y=x²-6x and the area bounded by the curve, its X-intercepts, and the…

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Q: A graphing calculator is recommended. (a) Find the equation of the tangent line to f(x) = x² - 2x +…

A: Solution

Q: use the washer method to find the volume of the solid of revolution generated by rotating the region…

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Q: Evaluate the integral. (Use C for the constant of integration.) The integral of 5dx/(1+cos(x))

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Q: 4. Let (x) - 6x² + 13x+7 3x + 2 What is the equation of the oblique asymptote of f(x)? From what…

A: Solution

Q: Based on the graphs of f(x) and g(x), what must the domain of (f. g)(x) be? 10 8 7 6 5 2 g(x) 1…

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Q: 1. For which values of a and b is the following system of equations inconsistent. x+2y3z = 4 3x - y…

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Q: The boundary of a lamina consists of the semicircles y = √1-x² and y = √25 - x² together with the…

A: Solution

Q: Suppose that the function fis defined as follows. -1 if -3.5<x< -2.5 0 if 2.5<x< -1.5 - f(x)= 1 if…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 1 1- Q2: Evaluate f ¹-² y² (x² + y²) dx dy the product

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Q: Find the volume of the solids generated by revolving the region bounded by the curves y = 7r² and y…

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Q: Problem 8. A function and its first and second derivative are given 2(2x + 11) f(x) = x² - 4 (x +…

A: As per guidelines, I can answer maximum three sub parts of a question. Here are four sub parts, so I…

Q: 6) Find The derivative of yo

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Q: A vector with magnitude 7 points in a direction 295 degrees counterclockwise from the positive x…

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Q: The graph below is the function f(x) 2 -5 -4 -3 -2 -1 2 B 4 -3 4 -5+1 Find lim x 2 Find lim 2 2 Find…

A: from graph limx→2- f(x) =-3

Q: Find AB using the following matrices: 7 8 1 2 3 A= B= 9 10 4 5 6 11 12

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Q: 20 18- 16 14- 12 10 8 b 4 2 1 2 Estimate the instantaneous rate of change at x = = 1

A: To find the instantaneous rate of change.

Q: Use the graph shown below to answer the questions. y 10 5 X 4 8 (a) Amplitude = (b) Period = X (C)…

A: This question is based on Sine function.

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: This question is related to series and sequence, we will solve it using given information.