Use a familiar formula from geometry to find the area of the region described and then confirm using the definite integral. r = 4 sin 0 +7 cos 0,0 ≤ 0 ≤ π. Area =

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A: The region bounded by the curves  and .The aim is to find the area of the region by integrating…

Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

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Q: lim       sin(π+h)- sinπ                                      h→0     —------------…

A: Note:-Since your part a incomplete ,please repost part a again(b)

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A: Given that f is a continuous function on the interval  and To find:-(f is even) (f is odd)

Q: Identify domain and range and determine it it’s a function

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5+ 4 3 2 1 -1 -2 -3 -4 -5+ 1 8 + 7 6 5 4 3 2 1 -1 -2 -3 3 -5 -6 -7 -8+ 4 The graph of a function y =…

A: The graph of a function  is shown. To make a sketch of theantiderivative F, given that F is…

Q: Find the area of the region bounded by the given curve: r = 7eº on the interval 4 -π ≤ 0 < 2π.

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Q: Consider the triangle below. Click on the picture to see it more clearly. If a = 8, the angle C =…

A: The given triangle has measures .The aim is to find the remaining meausres .

Q: 7. The sum of measures of the angles of a triangle is 180 degree. The smallest angle of the triangle…

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Q: Evaluate the following expression. log77⁹

A: ...(1)                         ...(2)

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A: The given equation of parabola is The vertex form of parabola with the vertex  is

Q: I need to find whether a series converges and if so I need to find the sum. the series is: the sum…

A: the series is: the sum from k=1 to infinity of 1/(16k2 - 4)

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Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

Q: Given that What is F'(x)? O Questi -S²³² F(x) = 3 In t t² +3 25x5 ln x x5 +3 5x² ln x x5 +3 9x² ln x…

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Q: 8. An engineer invests $27,000 in two bonds. If one 7% and the other yields 9%, how much is invested…

A: Let engineer invest $x on one bond which yields and  on another bond which yields

Q: 1-√x)³ 3 √x dx

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Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

A: The given equation is

Q: Let f(x) = 3x - 6 and g(x)=x+3. Find each composite function and describe the domain of the…

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Q: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: Find the area of the region between the curve and the x-axis. f(x) = 16-x², from - 7 to 7

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Q: A curve with polar equation r = 28 5 sin +41 cos 0 represents a line. This line has a Cartesian…

A: A curve with polar equation represents a line.To find the Cartesian equation of the line in the…

Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

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Q: The equation of a hyperbola is 64 a) Find the center, vertices, transverse axis, and asymptotes of…

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Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: 1. A rock is thrown upward with a velocity of 20 meters per second. Its height, in meters, t seconds…

A: According to our guidelines, we can answer only first question (due to multiple questions). Kindly…

Q: ate and classify all (by classifying the extrema, we mean listing whether locate any stationary…

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Q: The amount, A, of 159 grams of a certain radioactive material remaining after years can be found by…

A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

Q: If f(x) f'(x) = = x² S²³ to dt then

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Q: Rocky Mountain Tire Center sells 7,000 go-cart tires per year. The ordering cost for each order is…

A: a) Given that:Annual Demand (D) = 7000Ordering Cost (S) = 40Holding Cost (H) = 30% of Purchase…

Q: Question 12 Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers…

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Q: 37. se sec² (10x + 7) dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (c) (d) (e) creasing? Does g(x) have any critical points? If any, identify all critical points. On…

A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…

Q: 10. Find a function f such that F = Vf and evaluate ScFdr along the given curve C • F(x, y, z) =…

A: If there are two functions, a vector function and a scalar function that satisfies the following…

Q: Hello, can someone please help me with this calculus practice question

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Q: Evaluate the definite integral. 5 J 1+162 -dx

A: To evaluate the following integral.Note: Since you have posted multiple questions, we will provide…

Q: 5 Find an antiderivative of the function g(z) = = 23 An antiderivative is

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x, the line x = 4 and…

A: To find the volume of the solid obtained by rotating the region bounded by , the line  and the…

Q: Estimate the area under the graph of f(x) = 1+x² from x = -1 to = 2 using six rectangles and right…

A: Given,from x=-1 and x=2

Q: 6. Let So f(x) dx = 12, 5 Calculate the following integrals. (a) [°*3f(x)dx = (b) *2f(x) – g(x)dx =…

A: Let To calculate the following: (c) If  is an odd  function, then to find .Note:  Since, the student…

Q: K Sketch a continuous function f on some interval that has the properties described. The function f…

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Q: 2 2 Find the area of the region between the curves y = 4x² - 4 and y=-3x +3 from x= -1 to x= 1.

A: The required area is the shaded region in the graph

Q: (a) Find a power series representation for f(x) = (b) Use your answer in part (a) to evaluate the…

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Q: Evaluate the following integral. 2 | (0²-0 -2 (4y -6y+6) dy

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Q: Please answer the below quaestions: If f(x)= g(x)/ x,  and g(x)= x + sinx  ( interval 0, 2π) Find…

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Q: Given f'(t) = -0.4t+e-2¹, compute f(5) – f(3).

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Q: Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)) using…

A: Solution is following in explanation step.

Q: If the velocity of a car is given by v(t) = 90 for all time t ≥ 0, then the position of the car for…

A: The velocity of a car is  for all .The aim is to find the position of the car.

Q: Use l'Hôpital's rule to find the limit. Use -∞o or ∞o when appropriate. 3x²+5 lim x→∞04x³ +2 Select…

A: The objective of this question is to find the limit of the expression (3x²+5)/(4x³ +2) as x…