Find the sum of the series: Σ n=1 2 (n + 6)(n + 4)

Q: Refer to the graph shown below and evaluate Ĵ 1941 CH - 4 f(t)dt.

A: Consider the figure

Q: c. Which of the following expressions is equivalent to ln (10x²) for all values of x, including x <…

A: The given logarithm expression .The aim is to find the equivalent expression.

Q: 2. True or False: If the parametric curve x = a(t), y = b(t) satisfies d'(5) = 0 and b' (5) = 1 then…

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Q: Express your answer as a polynomial in standard form. f(x) = -3x + 5 g(x) = x² + 2x + 15 Find:…

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Q: A cup of coffee has cooled from 98°C to 50°C after 10 minutes in a room at 25°C. How long will it…

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Q: If f(x) = 15 to dt then f'(x) =

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

Q: A bacteria is known to increase a rate proportional to the amount present. After 2hours 1500 strands…

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Q: Find a power series representation for the function. f(y)=In f(x)= In[11+y)

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Q: Find the integral. Use C for the constant of integration. | cv² (y² + 3)² dy

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Q: After the release of radioactive material into the atmosphere from a nuclear power plant at…

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Q: Differentiate the functions: cosec x * cos x

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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: 5. Example: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the…

A: A graph of the functions  and  are given.The aim is to find the following,(a) (b) (c) Note:  Since…

Q: Find all exact solutions on the interval 0 ≤ 0 < 360°. If there is more than one answer, enter them…

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Q: Determine the moment of inertia of the area about the x axis. ' 2 in. 4y=x² T 1 in. X

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Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: Given,a(t)=t+4v(0)= 70=&lt;t=&lt;10

Q: Evaluate the indefinite integral. [(arcsin x)² √1-x² -dx

A: We have given indefinite integral-First let's define that-

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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Q: Find the Taylor polynomial of degree 3 of the function f(x) = arctan(9x) at a = 0. T3(x) = ||

A: f(x)=arctan(9x), a=0

Q: A water tank has the shape of an inverted cone with height 9 m and top radius 8 m. If V and h…

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Q: M8 ηχη n=1 3"

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Q: d. h(x) = x3 3 -2 - 2x² + 4x, 0≤ x < ∞0 e. f(x) = √25-x², -5 ≤x≤ 5 f. g(x) = 0≤x≤ 1 x-2 x²-1'

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Q: he letters x and y represent rectangular coordinates. Write the given equation using polar…

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Q: 7. Apply the test for divergence to each infinite series given below. Then using at least one…

A: Given:To Find: To apply the test for divergence, for each of the given series. Then to explain the…

Q: At what value(s) of x on the curve y=-7+90x^3-3x^5 does the tangent line have the largest slope?

A: y=-7+90x3

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: 7. An actuary invests $26,000 in two bonds. If one bond yields 12% and the other yields 7%, how much…

A: 7. An actuary invests $26,000 in two bonds. If one bond yields 12% and the other yields 7%, how much…

Q: Solve the following initial value problem. dr dy = x3 / x5, y(0) = 0 y =ㅁ

A: To solve the following initial value problem.

Q: 1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

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Q: Find the interval I and radius of convergence R for the given power series. (Enter your answer for…

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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…

A: The given equation is; 9cos(2t)=9cos2(t) -2, [0,2pi)

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: If f is continuous and f(x) dx = 12, find So f(2x) dx.

A: Given that To find

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x² −…

A: y=4−x2−ln⁡(12x+1), point (0,4)

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

A: To calculate the area bounded by the curvesy=x^3 and y=4x^2

Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y2 = −4y₁ + 1y2 where y₁ (0) = 4, y2…

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Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

Q: 1 se sec4 x tan x dx

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Trigonometric function can be used as parameterization of many curves, this is thanks to the use of…

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

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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

Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

A: The growth rate of population of prairie dog community is P(0)=50

Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = -1, v(0) = -7,…

A: Given that u and v are function of x that are differentiable at x=0At  To find:we have to find the…

Q: Let y = ln(1 + x²). Find the differential dy when x = 1.4 and dx 0.6. = Enter your answer as a…

A: Let .To find the differential  when .

Q: Find the equation for the line tangent to the parametric curve: at the points where t = 4 and t =…

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Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

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Q: Consider the following. f(x) = -3x² + 36x Find the critical numbers. (Enter your answers as a…

A: The objective of this question is to find the critical numbers of the function f(x) = -3x^2 + 36x…

Q: Consider the indefinite integral ax + b + where Then the integrand decomposes into the form C d a =…

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Q: Evaluate ∫∫∫E(x+y−3z) dV where E={(x,y,z)∣−4≤y≤0,0≤x≤y,0≤z≤x+y2}

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Q: Suppose we have a triangle with A 40°, B= 60° and c = 4. Then a =

A: Sum of interior angles of a triangle is 180 degrees