Find the value of k that makes the antidifferentation formula true [ (4x +1) 7 dx 4x + 1) ² dx = k ( 4x + 1) ³+ C

Q: Find the work done with a spigot 1m above a trough that measures 9m long and has sides that are…

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Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

Q: For the demand equation, express the total revenue R as a function of the price p per item q=-8p +…

A: Given that the demand equation is

Q: Determine the Fourier transform of the following signal: x (t) = è¯(t-1) u(t-1)

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Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Evaluate /² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: Use the given information to find the left- and right- hand Riemann sums for the following function.…

A: given function

Q: Consider the following vector field. F(x, y, z) = 4yz lnxi + (3x − 7yz)j + xy6z³ (a) Find the curl…

A: given vector field

Q: The table gives the annual US emissions, H(t), of "super greenhouse gases," in millions of metric…

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Q: Find the absolute maximum and absolute minimum of f(x) = 2x³6x² - 48x + 95 on the interval [1,6].

A: f(x)=2x3−6x2−48x+95 on the interval [1,6]Using the power Ruleddxxn=nxn−1

Q: Sketch a graph of x = -3 + cos(t), y = 3 + sin(t), 0 < t < 27 . -5 + 3 -2 -1 Clear All Draw: 5 4 3 2…

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Q: The following table shows the total sales, in thousands, since a new game was brought to market.…

A: Part (a): The data appear plotted with dots below:

Q: Current Attempt in Progress Incorrect. Find the area under P = 120(0.7)' between t = 0 and 1 = 6.…

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Q: 2. Sketch the graph of the quadratic y=- =-2(x+3)² +8 by using a series of transformations. Show all…

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Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = cos(x) on the interval [3π 5π…

A: 1) f(x) is continuous on [a,b],2) f(x) is differentiable on (a,b), and3) f(a) = f(b)then there…

Q: Evaluate u³(²-1)² du in terms of u by expanding the integrand. [/u³(²-1)² du = -/( 11 + C 1) du

A: To evaluate  in terms of  by expanding the integrand.

Q: C. Evaluate d²y dx² at the point (1,2)

A: Consider the curve

Q: Use the Second Derivative Test to find the location of all local extrema in the interval (-21,-9)…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Evaluate the line integral, where C is the given curve. Sext xªy√z dz, C: x = 5, y = t₁ z = t², 0 ≤…

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Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 &amp; x = 6

Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

A: The graph of derivative  is given below. To find the interval(s) on which the function  is concave…

Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

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Q: A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a…

A: The objective of this question is to find out what percent of the original amount of water…

Q: The surface whose equation in cylindrical coordinates is r = 5 is... a cylinder a cone half of a…

A: The given equation of is

Q: Find the length, L, of the curve from x = 4 to x = 6. 6 L° √ ₁ + 1 (F(x)² dx L = 6 - [5 /17 (× ² +…

A: Find the length, L, of the curve from x=4 to x=6.L=∫461+(f′(x))2dx

Q: Given the function f'(x) = −x³ – 6x² + 72x, determine all intervals on which f is decreasing.

A: If f'(x)&gt; 0 in an interval I then f(x) is increasing on interval I.If f'(x)&lt;0 in an interval I…

Q: (a) Use the figure to find the [ f(x)dx. value of L₁₂ f(x² f(x) dx = -10 f(x) Ax [ 1. 7 in (b) If…

A: We will find

Q: A. B. Explain how you could use the graph of y=x² to graph -1 y=x². Sketch the graph of y=x².

A: graph of  from

Q: For t> 0 hours, let r(t) = 120 (1 - e 5 liters/hour hour, at which a car travels along a straight…

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Q: 1. Region D of the (x, y)-plane is the locus of points satisfying the conditions 2y > e-* > y and y…

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Q: Given the acceleration a= initial velocity, and initial position of a body moving on a coordinate…

A: The given acceleration is.The aim is to find the .

Q: 2 X Estimate the error if P₂(x) = 1 - is used to estimate the value of cos x at x = 0.2. 2 |Error <…

A: To estimate the error in the given function.

Q: You are given the following pieces of information: 43 f (x) dx = -39, What is the value of 27 ² f…

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Q: √x csex² not x² dx 2

A: Consider the integral

Q: a) (D-2D + 5D²-8D + 4)y=0

A: In multiple question i can only answer first question as per company guidelines. Request you to post…

Q: I want to convert $600 USA dollars into the new euro currency.  The most recent WSJ currency Cross…

A: I want to convert $600 USA dollars into the new euro currency. The most recent WSJ currency Cross…

Q: Find the intervals of increasing and decreasing  for y= (sinx)/(2+cosx)

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Q: fx csc x² c X CSC csc x² cot x² dx

A: +C

Q: Find the values of a and b such that a = b + [¹ f(x) dx − [*f(x) dx = f*f(x) dx. - 11

A: Given,

Q: A) lim x²-x+1 5/3 x+2 3

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

Q: Evaluate the integral by interpreting it in terms of areas. 3 6.³ |2x - 3| dx

A: Simplify the absolute value of expression under integrand.

Q: Your velocity is v(t) = ln(t² + 1) ft/sec for t in seconds, 0 ≤ t ≤ 2. Find the distance traveled…

A: Velocity is v(t)=ln⁡(t2+1)ft/sec for t in seconds, 0≤t≤2.

Q: Ans. y=10 cost + 2 sint-√√2 sin√√2t 5. 2y+3y"-3y'-2y=e', y(0)=y'(0) = 0, y"(0) = 1 8 1 Ans. y 9 -1/2…

A: 2y'''+3y''-3y'-2y=e-t, y(0)=y'(0)=0, y''(0)=1

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: In the following exercise, given that 1 1-x = ∞ Σa x" for x < 1, n=0 use term-by-term…

A: Power series.

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: 4t² = [x(t) = ly(t)…

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Q: Question 4.21) Evaluate the following limits. sin² (1)-1 1-4 A) lim 2/2+1 B) lim x-0 Question 4.22)…

A: a) limx-infinity x[arc(tanx)-pi/2]According to Bartleby guidelines we solve only one question repost…

Q: Practice problems on section 9.5 Solve trigonometric equations: Solve the following equations on the…

A: This is question of algebraHere trigonometric equation are given We have to solve for x.Further…

Q: 4. Here is a graph representing a function of the form f(x) = a b*. Find the values of a and b. Show…

A: The exponential function is