Question ( the series ): What is the third term of 02/17 O-27 27 Select one: O None of them. n-1 Σ 25m (²3²³)" 5 n=1

Q: Compute the directional derivative of the function g(x,y) = sin((5x - 4y)) at the point P(3,3) in…

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Q: Find the derivative of the function f(z) = √2 O None of these. 37 Of(z) = √2z f(2)=

A: We will find the derivative.

Q: Find the limit (if it exists). If it does not exist, explain

A: A limit does not exist when limx→a-f(x) ≠limx→a+f(x)

Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: The table of values represents a polynomial function. X -3 -2 -1 0 1 2 -3 The function is a) quartic…

A: Let's find.  Table of value given.

Q: S 2 1-a Select one: O True O False e²e³dydx = - (₁ e²d²) (²* eºdy) (² dx 2

A: Given :∫01∫21-xexeydydx=∫01exdx∫21-xeydy

Q: Given f(x)=2+3x²-x² i. Find the coordinates of all local extrema. ii. iii. Identify the extrema…

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Q: The demand x is the number of items that can be sold at a price of $p. For x = p2² - 4p +600, find…

A: We can solve as follows

Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y=z²+1,…

A: To solve the following problem of finding volume using washer method.

Q: Use the properties of infinite series to evaluate the following series. 3. 5" Σ n=0

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: (g°N)(x) (fºg)(x) If f(x)= x-1 and g(x)= x², what is the first derivative of (f+g)(x) (g-n(x) +

A: To find out the derivative of the indicated function.

Q: tank

A: Please refer to the image below

Q: Use the price-demand equation below to find E(p), the elasticity of demand. x= f(p) = 15,000 -175p…

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Q: 2 4 23 4 4 f²f3x³y²dxdy = f²y³ dy fx¹dx Select one: True O False

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Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

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Q: Suppose F(z) = g(f(z)) and f(2)= 3. f(2)=-3, g(3) = -1 and g (3)=-4. Find F(2).

A: Recall: Chain Rule  Let F(x)=g(f(x)) , then F'(x)=g'(f(x)) f'(x)

Q: A machinist is required to manufacture a circular metal disk with area 588 cm². Give your answers in…

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Q: Recently, a certain bank offered a 10-year CD that earns 2.16% compounded continuously. Use the…

A: We have to find gross amount

Q: Choose the area of the region enclosed by: x = 0, y = 0, y = -x + 1. Select one: y-1 LL" dady O None…

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Q: The function z = Select one: O True O False f(x, y) has a local maximum at the critical point (3,-1)…

A: Given z=f(x,y) D(3,-1)=4 and fxx(3,-1)=-5

Q: Let V₁, V₂, and v3 be vectors in a vector space V, and let T:V R³ be a linear transformation for…

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Q: Question Determine the direction in which the graph of the following parabola opens. f(x)=(x-2)² – 5…

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Q: L4Q14.The first term of a geometric sequence is 18 and the common ratio is 2. Find the value of the…

A: Given first term and common ratio put these in recursive formula

Q: By using trigonometric substitution, evaluate the following integral IVF x √²+6x+10 dz

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Q: Consider the basis S = {V₁, V₂] for R2, where v₁ = (1, 1) and v₂ = (1, 0), and let T:R2 R2 be the…

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Q: When demonstrating that lim 5x + 3 = 8 with = 0.3, which of the following 8-values suffices? x →1 08…

A: limx→15x+3=8 with ε=0.3 We have to find the δ value.

Q: y(x) = 4x²y" + y = 0, y(-1) = 6, y'(-1) = 3 , x < 0

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Q: •√ (2x + √₁ (2r+√16-r²) dr by interpreting it in terms of areas. 10. Evaluate

A: Bh

Q: Which of the following is the critical point of the function f(x, y) = x²y = xy? - Select one: ○…

A: The given function is: fx,y=x2y-xy To calculate the critical point, we have to solve the equations…

Q: Use the functions below to find the given value. f(x) = x - 2 8 g(x) = x³ (gof)(-2) =

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Q: 17. √ ² √x (x²-3) dx

A: To evaluate the following integral.17 ∫01xx2-3 dx18 ∫-π22π sin x dx

Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

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Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Solve the given initial-value problem. dx dt dy = 25x - y dt x(1) = 0, y(1) = 1 x(t) = 0 = -11x - y…

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Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: For the function f(x) = sinx, where a = find the following. 6 a. Find the Taylor polynomials of…

A: Please see the below picture for detailed solution.

Q: Solve the given initial-value problem. y(x) = y" - 81y = 9, y(0) = 1, y'(0) = 0

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Q: . Consider the series partial sum of infinity to k = 2 of (k^4 + 2k^2 + k −3)^(1/2)/(k^3 + 2k^2 + 6)…

A: Solve the following

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: Simplify

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Q: The double integral √ √ ₁ (3. R (3x² + 2y), where R = [1, 2] × [-1, 2] is equal to Select one: O 18…

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Q: Find a linear equation that expresses the relationship between the temperature in degrees Celsius Ca…

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

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Q: Question Given the functions below, find the domain of (fog)(x). 1 -10x-7 Select the correct answer…

A: Here is the solution:

Q: Let R be the region bounded by y = 2x, y = 3 and - x = 0. Sketch the region R and evaluate the…

A: Solution is given below:

Q: Use the functions below to find the given value. f(x) = x 2 8 g(x) = x³ (g¹¹) (-2) = |

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Q: Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. f(x)= x³ -…

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Q: Given the double integral where D = {(x, y)| 0 ≤ x ≤ 2, 3 ≤ y ≤ 6}, then the iterated integral can…

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Q: The graph of y = f(x) is shown below (dashed curve). Manipulate the green draggable points to obtain…

A: Given data ÷ Graph of y=fx is shown with dashed line curve. We need to graph  y=2fx+1-4