Decide if a direct comparison test can be used to determine convergence of the following series. Explain your answer.

Q: Consider the following. x = t, y- In(t) (a) Eliminate the parameter to find a Cartesian equation…

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Q: Find the derivative using the definition 2х-3 y = 3x-2 What is the solution if the answer is: 2х-3…

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Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: The function g(x) is defined for-3 5xs3. The behaviour of g'(x) and g"(x) is given below. -3 <x<-2…

A: Given problem:-

Q: 1 1. Let f (x) = x - 5, g (x) = V5 - x and h (x) = 2x 1 a) Determine the domain of f, g and h. b)…

A: We have to find the function

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -175 feet per…

A: see below the answer and calculation

Q: Find the derivatives of f(x)=(ax4+b)6   and   f(x)=axe-bx+15 Assume that a and b are constants.

A: Given query is to find the derivative of the expression.

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: y²dy Vy2+4 3.

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Q: Screen Shot 2022-04-05 at 5.49.01 PM Q Search Problem #8: Demand for a certain kind of SUV obeys the…

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Q: Find all relative extrema of the function. Use the second derivative test to determine the extrema.…

A: We will find the relative extrema and the value of f"(2) as following. The function given f(x)=x^2…

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: Use implicit differentiation to solve the following related rate problems: (Include a properly…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: Consider the parametric equations below. x = 1+t, y = 1 - 3t, -2sts 3 (a) Sketch the curve by using…

A: Consider the parametric equation  x=1+t,y=1-3t,    -2≤t≤3

Q: 3. Herrera's ship is 70 kilometers due north of Arias' fishing vessel in a noon of a certain day.…

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Q: The base of a three-dimensional figure is bound by the x-axis and the curve y = e on the interval…

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Q: Using an appropriate lineař appratimation, Feel free to leave fractions in answer.

A: The given approximation 35

Q: 2. Y' = csc - y cot x ans. y sin x = x + C %3D

A: We know that; The standard form of the linear differential equation of first order is: dydx+Py=Q ;…

Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x +…

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Q: V y-2+1 dy

A: Please see the answer below.

Q: f(x) = sin° (tan(5e2*))

A: We can find the derivative as below using chain rule.

Q: Determine if the given function is continuous on the given interval a. [2,5) , x <O f(x) = %3D 5x-8…

A: To determine whether the given function is continuous on the given interval.Interval=[2, 5)fx=1x,…

Q: 2. The solution to the equation below is x = 2 and x = 5. cos? æ – 7 + 10 = 0 O True O False

A: The given equation is:

Q: 2. f(x,y) = ye3x²+4y³

A: Given query is to find the fist order partial derivative.

Q: Suppose the gradient of f (x, y) exists for all points in R2. Which ONE of these statements must be…

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Q: Solve the ff first order DE using integration method, by substitution, or bernoulli's equation. show…

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Q: x * - 2 and g (x) = 10. Given f (x) = x - 1X = 1. Find 2x + 1 a) the domain of f (x) and the range…

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Q: 4. f(x) = sin xand g(x) = 2x 5. f(x) = x² + cosx and g(x) = 3x + 4 Guide Questions: 1. How did you…

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Q: Consider the parametric equations below. x = 5t - 4, y = 4t + 2 (a) Sketch the curve by using the…

A: Consider the parametric equation  x=5t-4,  y=4t+2

Q: Consider the function f(t) = 3 sec?(t) – 4t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Let the cost function be C(x)= x2 / 8 + 4x + 200 and the unit is sold at price of p = 49 - x dollars…

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Q: How do you take the integral of 2 * sqrt(t^2 + 1) ?

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Q: V25x² -69 – dx

A: We will find the integral as following.

Q: Determine if the given function is on the given interval Continuous

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: funchoN f whose second derivative is f ")= 5x+2sin(x If fo 3 and fro)= 3. what is fe?

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Q: Answer the following about the function f (x) = (1/3)x^3 − (1/2)x^2 −2x + 1 1.Find intervals for…

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Q: (b) Given -3x + P for x7 Determine the value of p if f(x) is continuous at x=7. TEST DMI123

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Q: Given u(t) = (e',e-t). a) Find: (i) u'(t) (ii) u"(t) b) Find the unit tangent

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Q: y' + = 2x/y;;y(0) = 2 3. + 3x²y = 6x²; y(1) = -2 dx 4.

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Q: 1)Given that : f ( x ) = x3+9 x2/2 +6x-3 Find the critical numbers. b)Find the interval(s) where…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: The base of a three-dimensional figure is bound by the circle x2 + y? = 9. Vertical cross sections…

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Q: 1 x (In x)3

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Q: Find the open intervals on which the function is increasing or decreasing. Apply the First…

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Q: V3 - 2s ds 02 40

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the radius of convergence about x = -2 and interval of convergence of the series Sn°(ar + 2)"…

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Q: What is the reference angle of O if 0= -137°? A 43° B 47° C 137° D 223°

A: Given query is to find references angle.

Q: - ſ csc²e cot êī – 5 cot ê dê

A: