Determine the value of the following definite integral. St dz 15x+20x³ 3x²+2 Leave your answer in exact form, for example: 3 (In 6 - In 4).

Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

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

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A: There are three different questions given. As per our company guidelines, we are supposed to solve…

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A: Given that the triangle we have to find choose the correct option

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Q: Find the area of the region between the curve and the x-axis. 2 f(x)= x(x² -26), from - 5 to 5.

A: The region is bounded by curve  and x-axis from

Q: Solve the following problem and show your complete solutions. 3. Find the area bounded by y = x³ ; y…

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Q: Find the area of the blue region. It is the area under the curve. y 8 6 4 2 y = 3x + 1 y=8-x

A: We have to use the concept of definite integral

Q: For answer in part "E", is the answer 1/2 ln| sqrt(x^2+4/x^2) - 2/x |+C or 1/2 ln| sqrt(x^2+4) / x^2…

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Q: Consider the following. f(x) = 48x − 4x2 Find  f '(x). f '(x) =        Find the critical…

A: The objective of this question is to find the derivative of the function f(x) = 48x - 4x^2 and then…

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = 6t², y = 4t³,…

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Q: 9. In the following exercise: i. Identify the function's local extreme values in the given domain,…

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Q: (a) Find expressed as a function of t for the given the parametric equations: dy dx dy dx d²y dx²…

A: Given: To Find: (a) To find .(b) To find .

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Q: Let xy = 4 and dx dt Find dy dt when x = = 2. 1.

A: ..........(i)Differentiating equation with respect to t Put   ..........(ii)

Q: 2. For the function g whose graph is shown, state the following. (b) lim g(x)= x-0 (a) lim g(x)=…

A: The graph of the function is given.The aim is to find the e)The equation of the vertical asymptotes.

Q: Find and simplify the difference quotient f(x) = 8 f(x+h)-f(x) h h#0 for the given function.

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Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

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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: 7. Evaluate the definite integral. a. b. С. 9 cos(xt/2) dt в'ітетка 1+ * = dx 47 dx

A: The given intergals are

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Q: Find all exact solutions on the interval [0, 27). If there is more than one answer, enter them as a…

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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: The compound amount, A, accrued with continuous compounding is given by A= P.100.4343rt, where P is…

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Q: Express your answer as a polynomial in standard form. f(x) = 2x² 5x – 12 - g(x) -2x + 2 = Find:…

A: f(x)=2x2-5x-12g(x)=-2x+2

Q: for Integrals Find or approximate all points a which the given function equals its average value on…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: g. y = ex² +1 h. y = esinx y = ln(sin x) i. j. y = ln² + e√x X 6. L

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Q: Find a, b, c, and d such that the curve y=ax^3+bx^2+cx+d has its tangent line at (1, 1) and at (0,…

A: To find such that the curve  has its tangent line at(1, 1) and at (0, -2) are parallel to lines…

Q: Given f'(x) = 6x + 5, compute f(4) – f(1). -

A: Explaination of the answer is as follows

Q: Find the area of the region pictured below that is bounded by the functions v(y) = 3y – 6, u(y) =…

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Q: Find the indefinite integral. J (100e5x) dx = +C

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Q: f(x)=x^[8/3]-4x^[2/3] determin the: a) roots b) Domain c) intervals for which the function is…

A: The given function is To find:-rootsdomian intervals for which the function is positive and negative…

Q: Express the function as a power series by first using partial fractions. f(x)= 2x+5 x2+5x+4

A: Given: f(x)=2x+5x2+5x+4let's first factor the denominator and then use partial fractions.The…

Q: Find the domain of f(x). f(x)=√x² + 9x - 8

A: Here we will find the domain of the given function on solving the quantity under root putting…

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Q: 13. If there are initially 2000 bacteria in a culture, and the number of bacteria double cach hour,…

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Q: Consider the parametric curve: x Y 4 +² +³4t At which t value(s) is the tangent to this curve…

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Q: Find the domain of f(x). ƒ(x) = √√x² − x − 12 Answer Attempt 1 out of 2 Answer Type: Interval…

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