Find a formula for the nth partial sum of the series and use it to determine if the series converges or diverges. If the series converges, find its sum. Σ (1)

Q: The function f(x) = 2x³ − 42x² + 270x - 7 has two critical numbers. Use the derivative to…

A: we are given the function and we need to find the critical numbers.

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A: The given function .The aim is to find the value of the derivative .

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Q: Differentiate the function. y' = y = (In(1 + e*))5

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Q: 8. A = [₁ 2].B= 0 3 -5 1 2 4 3 -1 6 045 0

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Q: Let f(x) = lnx Since f(x) rs for x>0 Continuous Since (1,1,04), by mean such that on [1, 1.04] and…

A: The given function is

Q: -4 -3 -2 -1 4 3 2 1 -1 -2 -3 -4 1 2 3 4 20x For the above rational function f( x ) = 3.5r2 +3…

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Q: Simplify the rational expression. 9x³ - 36x² + 6x - 24 16 - x²

A: we need to simplify the given rational expression.

Q: 11. A conical water tank with a vertex angle of 60° is being filled with water at a constant rate of…

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A: We solve the given problem by using the concept of the ellipse.

Q: Find the exact length of the curve. 36y² = (x² - 4)³, 2≤x≤6, y 20

A: Find the exact length of the curve.36y2=(x2−4)3,2≤x≤6,y≥0

Q: 4. §11.5. Q10. Use appropriate form of the chain rule to find dw/dt. w = √√√1 + x2yz¹x; x = ln t, y…

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Q: For any two nonparallel vectors a and b, it holds that Select one: O 3a + b 3|a| + |b| O|3a + b =…

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Q: Write a fraction to represent the shaded portion. Need Help? Read It

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Q: 4. A = -1 0 5-2 245 0 -3 , B= 7 650 -3 -4 2 -1,c=7,d=5 7 9

A: we are given the matrices and we need to find out the matrix cA+dB

Q: 2. (a) Find the slope of the tangent line to the curve f(x) = 2x³ - 3x at x = -1 using a definition…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Determine the direction in which the graph of the following parabola opens. f(x)=−5x^2+x+4 Up Down…

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Q: Evaluate the integral Scos³ 40 Sin 80 de

A: Given Indefinite integral as follows As we know that

Q: 1. Evaluate each 2-variable function f : D → R below at the given points. For a point described with…

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Q: In 2004, an art collector paid $155,328,000 for a particular painting. The same painting sold for…

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Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

Q: If h(a) = h(b), then what is the value of ·b [ g(h(x))h' (x)dx

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Q: Compute the curl and divergence of the vector field F(x, y, z) = (1, 2², 2yz). 1+x² Is F…

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Q: 2. Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water…

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Q: Find the exact directional derivative of the function √y z at the point (1,9, 9) in the direction…

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Q: Determine the derivative of the following function with respect to a: 75 +¹rsin (r) 4,

A: f(x)=π5+π4xsin⁡(x)

Q: -7-6-5-4-3-2-1 1 2 3 4 5 6 7 Draw the graph of y = f(2x+4) -3 by adjusting the vertex and width with…

A: given graph of function f(x)

Q: Find the point where the tangent line to y = 5x² at x = 0.7 crosses the x-axis. x-intercept =

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Q: Solve e³t = 1800 for t.

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Q: A new music company wants to start selling col л(p) 100p-2.5p², where p is the price of a collection…

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Q: 1. Let g(x) = ln ((f(x))² + x). Determine g'(5) if f(5) = 2 and f'(5) = 3.

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Q: Suppose the demand for a product is given by D(p) = −4p + 111. A) Calculate the elasticity of demand…

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Q: Set up, but do not evaluate, an integral for area of the surface obtained by rotating the curve…

A: To set up, but not to evaluate, an integral for the area of the surface obtained by rotatng the…

Q: Find the derivative of the following functions using derivative rules. A) f(x) = x5 f'(x) = B) f(x)…

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = x5 e-x (a) Find the…

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Q: A particle moves according to a law of motion s = f(t), t≥ 0, where t is measured in seconds and s…

A: A particle moves according to a law of motion .where t is measured in seconds and s in feet.(e) To…

Q: 5. Recall that y = sec-¹x (with domain x ≥ 1) means sec y=x and 0 ≤y</2 or T ≤ y ≤ 37/2. Use…

A: To prove

Q: In 2005, a school population was 1708. By 2006 the population had grown to 1776. 1) How much did the…

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Q: The function f(x) = -3√x - 15 +14 x > 15 has an inverse f-¹(x) defined on the domain x < 14. Find…

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Q: Find and simplify the derivative of the following function. f(x) = 25xe x -X The derivative of f(x)…

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Q: 1a)Using a ruler, draw the xy-plane, and then sketch the graph of arctan(x) onto this plane. As…

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

Q: Find the derivative of the function. f(t)=√3+ tan(t)

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Q: Given the demand function D(p) = √100 - 3p, Find the Elasticity of Demand at a price of $17 At this…

A: Elasticity,E(p) = Where D(p) is the demand function.

Q: Differentiate. g(t)=31t g' (t) =

A: To differentiate the following function.

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Q: Write an equation for a line perpendicular to y = 5x - 4 and passing through the point (10,-7) y=

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Q: Write an equation for a line parallel to y - y = 2x 3 and passing through the point (2,0)

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