Using Part I of the Fundamental Theorem of Calculus, evaluate: d d.x 10 t³ dt =

Q: 1 4. fv³ (a²-v²) dv

A: Given problem:- ∫v3a2-v212dv

Q: Question 4 Find the power series for 2xe² by differentiating power series representation of ex. Also…

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Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

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Q: Use the Limit Comparison Test to determine convergence or divergence. 3n²+ n=1n²+5n²-7 ∞ Σ Select…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the following piecewise function ƒ : R → R 3.2³ 7.x 8x²730 f(x) = Indicate which of the…

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Q: Solve the problem. 57) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out…

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Q: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-

Q: attatched

A: Topic:- application of integration

Q: Express the given quantity in terms of −sin x or cos x. sin(3ℼ/2 - x)

A: The given trigonometric function is f(x)=sin3π2-x

Q: What is the equation of the standard hyperbola with vertices at (0, ±a) and foci at (0, ±c)? Choose…

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Q: 2. √a²-x² dx x2

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Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, A = with…

A: This is  a problem related to integration of polar coordinates.

Q: 3. Determine whether or not the series converges. Justify your conclusion. 86 Σ n=1 n² - 2n n³ + 3n+…

A: Solution is given below:

Q: Using the differential length dl, find the length of the curve. r = 1,0 = 30°, 0° ≤ Ø ≤60° O O 1.530…

A: Given Problem:- using the differential length dl, find the length of the curve  r=1,θ=30°,0°≤ϕ≤60°

Q: Find the breakeven point of the following functions: C(x)= 4x +4 R(x) = 6x Approximately (2, 12)…

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Q: Answer the following True or False: If p(x) and g(x) are polynomials such that p(4): O True O False…

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Q: Find the limit of the following sequence or determine that the sequence diverges. {(₁+)⁰} Select the…

A: We have to find the limit of sequence if given sequence is convergent and also we have to find the…

Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship…

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Q: the blank(s) provided. 9. The y-intercept of the function f(x)=4(2) is 10. To the nearest hundredth,…

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Q: Compute the definite integral as the limit of Riemann sums. (4x - 1) dx 47) 1

A: We will be answering the first question as per the guidelines.

Q: Find the function represented by the following series and find the interval of convergence of the…

A: We have to interval of convergence

Q: Which line has the greatest slope?

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. [][₂₁x² +…

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Q: Water is leaking out of an inverted conical tank at a rate of 11700 cubic centimeters per min at the…

A: Let's find rate of water is being pumped into the tank.

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

A: The objective is to determine the average rate of change for the function.

Q: Consider the following. Function y = 7e1 - x2 (a) Find an equation of the tangent line to the graph…

A: Solution

Q: Write the equation x = -5y^2 in polar coordinates and state values of theta that produce the entire…

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: Topic = Derivative

Q: 3. Determine the equation of the tangent to y = x² + 6x + 9 which has a slope of 6. Sketch the graph…

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Q: The graph of a function f is given. Use the graph to estimate the following. local maximum local…

A: Please see the below picture for detailed solution.

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: Find the limit of the following sequence or determine that the sequence diverges. 6n {(₁+3) ⁰}…

A: We have to find the limit of the given sequence.

Q: 9 4 Let C₁ be the ellipse + - 1 traced counterclockwise and C₂ be the paral- lelogram with vertices…

A: Consider the following diagram with the given curves and their respective orientations:  Note that…

Q: estimate the area under the graph f(x)=2x2+1   from x=0 to x=2 use four rectangle and the right…

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Q: Find the equation of the parabola described below. Find the two points that define the latus rectum,…

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Q: If the odds in favor of E occurring are 2: 7, then find P(E) and P(E'). P(E)= (Type an integer or a…

A: If the odds in favor of E occurring are 2:7, then to find PE and PE'.

Q: What is the best equation for the following scenario? A mountain climber starts at the bottom of a…

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Q: Estimate the area under the graph of the function f(x)=√x + 4 from x = -1 to x = 2 using a Riemann…

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Q: Consider the function f(x) = 2x² - 6x +7, 0≤ x ≤7. The absolute maximum of f(x) (on the given…

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Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

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Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

A: The objective is to solve the above question.

Q: breakeven

A: A point (x,f(x)) is said to be break-even point if revenue is equals to cost.

Q: Use the Ratio Test to determine if the series converges. 8 Σke-8k k=1 ... Select the correct choice…

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Q: Use the Root Test to determine whether the series converges. Σ k=1 1 In (k+14) Select the correct…

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Q: What are the coordinates of the x-intercept of the equation 2x - 3y = 8? (-4,0) (-8/3,0) (0,-8/3)…

A: Please see the below picture for detailed solution.

Q: K Write an equation for the ellipse. Type the left side of the equation in the box below. Q

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Q: Write an exponential mathematical equation to justify the statement log, (54) = 2.87744. Answer:

A: given, log454≈2.87744

Q: Find the maximum value of the parabola using the following equation: f(x)=-x^2+4x+3

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