Which one of the following is an antiderivative of the function f(x)=sec² (2x+1)

Q: Use Green's Theorem to evaluate the line integral. by² dx + xy c C: boundary of the region lying…

A: The objective of the question is evaluate the definite integral using Green's Theorem.

Q: Find f'(x) and f'(c). Function f'(x) = f'(c) = f(x) X-7 Value of c c = 1

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Q: Use sigma notation to write the sum. 1 7 (2) + 7 (3) j = 1 1 7(1) + 1 7(10)

A: The given sum 171+172+173+.....+1710

Q: sketch and find the area of the region enclosed by the graph of the equation r=3 cos Θ....

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Q: The polar coordinates of a point are (12, coordinates of the point. ○(-6√3,6) (6,-6√2) O O (6,-6)…

A: We have to solve above question

Q: Question d²2 y dx² Find dx² if -9x² - 5y² Provide your answer below: = = -3.

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Q: The temperature at time t hours is T(t) = -0.3t² + 4t + 50 (for 0 ≤ t ≤ 12). Find the average…

A: Topic-Average Value of a function over an interval

Q: Find the exact length of the polar curve. r = 3 sin(0), 0≤0 ≤ π/4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find F as a function of x and evaluate it at x = 0, x= x/4, and x = x/2. - L'sin F(x) = F(0) = (4)…

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Q: Provide your answer below: f'(8) = |

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Q: (22) Graph f(x) = e. (23) Let f(x) = e. Then, it is an • limx→∞ f (x) = and lim (24) Find lim, f(x)…

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Q: Question 1 Determine if the function below is continuous at x=9. Give reasons for your answer. F(x)…

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Q: Evaluate ₁² 2¹-132²+¹ dx .

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Q: Examine the function f(x, y) = x³-27xy+y³ +6 for relative extrema and saddle points O relative…

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Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

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Q: Find the second derivative of the function. f(x) = x cos(x) f"(x) =

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Q: Evaluate the following expressions. 2) cos [2Aresin (-) + Aretan (1)

A: cos2sin-1-12+tan-134

Q: Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2π). (Enter your…

A: The general solution of cos θ = cos x  is : θ = 2nπ ± x , where n ∈ Z.

Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

A: answer is in next step. please give a like!!

Q: Use Euler's Formula to express each of the following in a + bi form. (Use symbolic notation and…

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Q: Use the given conditions sin(8)= - 4' to find the values of all six trigonometric functions. (If an…

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Q: ) Use the Integral Test to determine whether the infinite series is convergent.   ∞ 7n (n2 + 1)3/5…

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Q: (a) Write a function of the form P (1)=Poe to model each population P(1) (in millions) f years after…

A: Consider the table

Q: Write the first five terms of the sequence defined recursively. a₁ = 5, ak+1 = 4(a-3) ak+1 a₁ az 33…

A: We will find the required.

Q: Find f" (1/2) when f(x) 2x+3. Round your answer to three decimal places.

A: To find f''12, when fx=2x+3.To round the answer to three decimal places.

Q: Find the exact value of the trigonometric expression given that sin(u) = - sin(u + v) Need Help?…

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Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

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Q: Find the area of the region common to the circles r=-6 sin 9 and r= 3.

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Q: 3. The rate of decay in the mass, M, of a radioactive substance is given by the differential…

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Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

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Q: 2 Consider the function f(x) = x+61 3. (a) Find the domain of f(x). Note: Use the letter U for…

A: "since you have posted a question with multiple subparts , we will solve first three subparts for…

Q: Find the unit tangent vector T(t). r(t) = 1²₁ + tj + 201 k, T(5) = P(25, 5, 20/3) Find a set of…

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Q: What is the slope of the line 0 = ? (Use decimal notation. Give your answer to three decimal…

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Q: Find r(t) given the following. r'(t) = 18t5j+20t¹k, r(0)=2i+18j O r(t)=2i+(18+ 3t6)j + 4t³k O r(t) =…

A: Given,

Q: The position vector r describes the path of an object moving in space. Find the velocity v(), speed…

A: Given r(t)=etcos(t), etsin(t), et

Q: Find f" (1) when f(x) = x² − 3x³ + 2x² +10. Round your answer to three decimal places, if necessary.

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 10+ 0…

A: Given that, the function is 3x+4y=24. Rewrite the given function as follows,…

Q: d. projab

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Q: 12. The trigonometric identities applicable to evaluate [sin' e cos³0 de 1 III. sin² 0 = (1-cos20) 2…

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Q: Assume that and y are both differentiable functions of t and are related by the equation y =…

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Q: Evaluate the integral using the following values. 1x30 ³x³ dx = 960, 3 f(x-15) a x xax = 24,ax = 4

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Q: Let f(x) be a smooth and continuous function. If f(x) has a local maximum at a = a, then whic of the…

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Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices:…

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Q: (4) Draw the graph of the function f(x) = 2¹. (5) Draw the graph of the function f(x) = 3.

A: Consider the functions 4)     f(x)=2x5)     f(x)=3x

Q: n (² f(x) dx Jo Given f(x) dx = 11 and "f'rx (a) f(x) dx. (b) Irox f(x) dx. (c) for f(x) dx. (d) f³…

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Q: Revenue The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research…

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Q: Find dy/dx and d²y/dx². dy dx d²y dx² 11 || x = t² + 9, y = t² + 3t For which values of t is the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: Question Given f(x)=2₁, find f' (3) using the definition of a derivative. Provide your answer below:…

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Q: Use Euler's Formula to express each of the following in a + bi form. (Use symbolic notation and…

A: Euler's Formula eix=cosx +i sinx