2. Given the first 5 terms below, write down the general term of the following sequences: (a) 80, 74, 68, 62, 56...

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² − y³ )dy = 0 is

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Q: A circle is inside a square.

A: Let a be the side of square and r be the radius Let A be the area enclosed between the circle and…

Q: Use partial fractions to find the indefinite integral. (Remember to use al 9-x2 10 dx 5x³ + x

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Q: Evaluate the integral of the following using Miscellaneous Substitution

A: We have to find the integral.

Q: Let f(x) = 5 on [−3, 1]. x+5 Find all numbers c in [-3, 1] for which the derivative is equal to the…

A: We are given a function f(x) = 2/(x+5) on [-3, 1].   We have to find all the c in [-3, 1] such that…

Q: Find all solutions of the equation in the interval [0, 21). COS +1=0 2x 3 Write your answer in…

A: This is a problem related to trigonometric identity. Based on the given interval and function…

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Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t p j+126t2 k, 3≤t≤6

A: r(t)=t3 i +t j+126t2 kdxdt=3t2dydt=1dzdt=252 t3≤t≤6

Q: 1. fx² In x dx = f x² dx f In x dx (In x − 1) + C Is the solution correct? If your answer is yes,…

A: We have to give reason and then solve the integration .

Q: Evaluate the integral [₁ F. dr. F(x, y) = (x² + y) i+(6x - cos y) j where Cis the boundary of the…

A:

Q: In ( ;). Find for. z = ln Əz Əx

A: Given that       z = ln(x/y)

Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + 1²j|| dt = |

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Q: Find the exact area under the graph of f(x) = = and x = 2. Area = 1 x+1 between r=0

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Q: 1. x²y' + 2xy-5y³ = 0

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Q: Let f(x) = x² - 1 on [-2, 3], Part A: What is the slope of the secant line connecting the function…

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Q: Solve for the solution: (4D3-13D+6)y=0

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Q: Using Disk Method solution, R is bounded by x-axis, y-axis and the line 2x + 3y = 1. This is…

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

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Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

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Q: Find the equation of the tangent line to the graph of f(x) = 5 sin(x) + 6 cos(x) at x = equation: in…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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Q: The angle below subtends an arc length of 5.52 cm along the circle centered at the angle's vertex…

A: We know that θ=lr⇒θ=5.522.3=2.4 radians.

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

A:

Q: Evaluate 1.1² (2x − y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (3, -5)

A: Solving

Q: Solve the following X 1.0[₁-2x] i. D ii. D[xln (2x) ] iii. D[cosx – 3 sin (2 x) ]

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Q: 2. Determine the area of the region bounded by the curve y = x³ - x² - 2x, and a. the x-axis the…

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Q: specu A cyclist is riding a bicycle whose wheels have a diameter of 20 inches. Suppose he is…

A: We have to calculate angular speed and revolution.

Q: Question 20 Find the derivative of y = log₂ (x - 2)³ 1/(In2)(x-2) 3/(In2)(x-2) 2/(In3)(x-2)…

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Q: = cot = C C In (x² + y²) + 4 arccot =

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Q: second derivative tests. =) has a relative Choose one Choose one maximum minimum at the point (?, ?)

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Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

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Q: A farmer uses a lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

A: Given R=700-400e-(x/100)

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: 15 Find sin 2x, cos 2x, and tan 2x if cosx = 17 and x terminates in quadrant I.

A: Given that  cos x = 1517 and x terminates in quadrant I. We have to find  sin 2x, cos 2x, and tan…

Q: XB-5 \\f(x) #3 g(x) Find the area enclosed between f(x) = 0.6x² + 10 and g(x) = x from x = −5 to x =…

A: The given problem is solved below in detail.

Q: Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

A: Given

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C' is oriented counterclockwise.…

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Q: Find the area of the region that is enclosed by the cardiod r = 10 - 10 sin 0. NOTE: Enter the exact…

A: Given:       r=10+10sinθ  Area of cardiod A=∫∫Dr dr dθ…

Q: 6. Consider the circle (x - 2)2 + y² = 1. Sketch the surface obtained by rotating this circle about…

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Q: Suppose that z = x²y³, where both x and y are changing with time. At a certain instant when x = 2…

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Q: Describe the graph of the equation. r = (8-2) 1+ 14tj It is a line in 2-space through the point…

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Q: Find the volume generated when the area in this problem (Find the volume of the solid generated when…

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Q: long as 1 235 times as long 235 times as long 235 times as long 360 235 times as long 2π 360 times…

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Q: Solve the solution: (D2 - D - 2)y= cos x

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Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

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Q: (3x+4)2dx Evaluate indefinite anti-differentiation

A: The given integral is (3x+4)2.