Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √√1+3x, 1≤x≤9 Need Help? Watch It

Q: Calculate the gradient of f(x, y) = cos(x² + 3y) Vf= ←

A: We have to find the gradient of the given vector.

Q: lve √√-36 de by using trigonometric substitution x=6seco..

A: Given Integral:- ∫x2x2-36dx

Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: 2. 3 (D-9)³y=0

A: Let's solve given diffential equation.

Q: Chapter 14 Review 57: Find the minimum and maximum values of f(x, y) = x²y on the ellipse 4x² +9y² =…

A: Given function:- fx,y=x2y Let gx,y=4x2+9y2-36

Q: 2 S (9x² - 4x + 1) In ada = (A) B C (D) 4 ln 2- - 19 2 18 ln 2-7 18 In 2-5 36 In 2-18

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Q: The total cost (in dollars) of producing a coffee machines is C(x) = 2400 + 60x -0.2x². (A) Find the…

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Q: 1.1. Evaluate the following integrals: a. ²x dx b. (2x+3)√2x-1 dx

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Q: Using test points from the original function give where the function is i 0x1 0x1 Ox>-3 Ox 1 x < 1

A: Solve this function by taking derivative greater than zero

Q: solution to evaluate 3 2+1 y-1 ГГГ x + y2 dx dy dz ? Z 3 4 Ⓒ √ ²² - ² - ² + + 2+1 A 6 2 2 В 3 o fl с…

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Q: In problems 3-5, use the building block n=0 Σ", <1, together with the result differentiating and…

A: Note : As per our guidelines , we can solve first question . Please repost remaining question .

Q: Find the linear approximation of f(x) L(x) = -7x = 9e at x = 0. Then use your linear approximation…

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Q: We conclude by showing the max and minimum points. maximum (2,26) minimum (1,1) maximum (-2,-26)…

A: d dx(xn)=nxn-1for critical points  put f'(x)=0fot critical values of x  if  f''(x)&gt;0  minimum and…

Q: Example: A point is moving graph of y²-3x²= 13, where yz0, so that at the moment when the…

A: Given Equation:- y2-3x2=13

Q: Compute the radius of curvature a the curve x=2y^2-3y at (4,2). 97.15 O 6.63 O-97.15 O -6.63

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Q: 2. A 71.6m tower is to be constructed on a hill with a slope of 15.6°. Both cables make a 42.5°…

A: We will use sin Rule to find the length of each cable.

Q: Let f(x) = 2x + x 100

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Q: Find the slope of the following lines.

A: see below the answer and calculation

Q: Graph the line with the given point and slope. Using the format of graph in picture. 1.) (-6,4);m=…

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Q: Consider the function below. In x 9√x (a) Find the interval on which f is increasing. (Enter your…

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Q: Find the derivative of the function. g(x) = 4x² 1 tan(x) V7+ 4 dt

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Q: X Dx f¹2dt 4+t -X

A: We have to differentiate the given equation.

Q: 9y" y(0) = 2 y'(0) = -1 12y + 4y = 0

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Q: or a certain company, the cost for producing z items is 55x + 300 and the revenue for selling z ems…

A: Given query is to find the profit function and the value of x when profit is $50.

Q: couple believes they can afford a monthly house payment of $2,100 and would like a 30-year…

A: Given query is to find loan amount.

Q: Select the factored form of the expression 3x² - 11x-4.

A: factor: 3x2-11x-4

Q: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the…

A: Given : A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch,…

Q: Find the critical points of the function x3 ² + 2x² - + 2x² - 12x. 3 Use a comma to separate…

A: for critical points  f'(x)=0d dx(xn)=nxn-1

Q: Find an equation of the tangent line to the given curve at the specified point. е e6x y-of (1₁60) у…

A: Given query is to find the equation of the tangent.

Q: Consider two nonnegative numbers x and y where x + y = 11. What is the minimum value of 7x² + 13y?…

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, P4(x) = c = 7

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Q: Question 1 Evaluate the integral. 2xsinxcosxdx Ax cos 2x - sin 2x + C B-x cos 2x + sin 2x + C C) -x…

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Q: If $6,000 is invested for 5 years at 8% compounded quarterly, how much interest (in $) will be…

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Q: List the first five terms of the sequence. an = cos(n) 1 a2 a3 a4 a5 || = || = =

A: We have to solve given Questions.

Q: All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a…

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Q: Find the slope of the following lines.

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Q: 1) Use the Comparison Test to determine whether the infinite series is convergent. ∞     k = 2…

A: Comparison Test:- If a series of the form ∑n=1∞an is given. Also if we know that ∑n=1∞an≤∑n=1∞bn…

Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

A: Given query is to apply rolle's theorem.

Q: Which of the following is equivalent to 2x + 5 S (2-4x) 5 after appropriate algebraic substitution…

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Q: 71-2 1 √n Inn

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Q: Problem 6. A particle is moving on a horizontal line. Its distance from the origin at time t20 is…

A: The  particle is moving to the left if the velocity is negative.

Q: Find the 10th derivative of the function: y = (x+1)/(x-1)

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Q: The area of an ellipse with axes of length 2a and 2b is A = tab. Approximate the percent change in…

A: Topic = Area

Q: The figure above shows the graph of the continuous function f. The regions A, B, C, D, and E have…

A: The area of region A =5It is above x - axis therefore, ∫-7-5f(t)dt = 5The area of region B =2That is…

Q: The supply and demand for a product are given by 2p - q = 100 and pq = 300 + 25q, respectively. Find…

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Q: The weight of a lake trout as a function of age satisfies the formula where Wis in kg and t is in…

A: The weight of a lake trout as a function of age satisfies the formula Wt=241-e-0.22t3 We have to…

Q: Evaluate the following definite integrals using the basic rules (and change of variable, if…

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Q: (a) A water container, whose circular cross section is 6 ft in diameter and whose height is 8 ft, is…

A: Given:    A = area of the tank a = area of bottom hole…

Q: Let U = 3i−j−4k and V = −2i+4j−3k. Show that U·V is commutative but U×V is not.

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Q: (a) Using algebraic division and integration by substitution, or otherwise, show that - dx = e² −…

A: We can evaluate the given integral by using the substitution u = ex