Evaluate the integrals. Making use trigonometric Substitutions. dx (a^² + x²³²) ³/2₂ St

Q: 1. Find the average rate of change of f(x) = x² -2 on the interval [-4, 8]. Then find the x-value…

A: To find out the average rate of change of function on the interval.

Q: Il Find the acute angle between two tangent lines at point of intersection between two curves xy = 5…

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Q: Use the Fundamental Counting Principle to solve:In the original plan for area codes in 1945, the…

A: Given data:- The first digit could be any number from 2 through 9 The second digit was either 0 or 1…

Q: Find the required value by setting up the general equation and then evaluating. Find s when t-4.0 if…

A: Given:s is inversely proportional to the square of t.Ands=3 when t=8

Q: 2. Consider the following system of equations. x+y-1 2x²+2y² - 4y - 6 = 0 = 0. a. Transform the…

A: Given two equations. x+y-1=0 2x^2+2y^2-4y-6=0

Q: 22. (e¹ + y) dx + (2 + x + ye³) dy = 0, y(0) = 1

A: Given ex+ydx+2+x+yeydy=0 and y0=1

Q: The two open disks B((1, 2); 2) and B((-2, 1); 2) has intersection. True False

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Q: If f(x) = f'(x) = ƒ' (3) = 6x + 7 2x+6' find:

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Q: Let's say you are shopping for a sofa this weekend with a budget of no more than $400. Inside a…

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Q: Consider the function f(x, y) = (eª — x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a…

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Q: ng the table below. 3 4 3 1 4 3 3 2 1 2

A: We have to find the value of the given following conditions according to the given information

Q: What is meant by an increasing function? A decreasing function?Give an example of each.

A: Increasing and Decreasing Functions in Calculus:- Calculus uses a function's derivative to…

Q: A car rental agency charges $200 per week plus $0.20 per mile to rent a car. a. Write an equation…

A: Given data : Car charges by rental agency $200 per week and $0.20 per mile to rent a car.

Q: Set f(x) Question 1 Solve the equation f'(x) = = 0. If there are more than one solution, separate…

A: Explanation of the answer is as follows

Q: Eliminate the Arbitrary Constant in the ff. equations: 2 b. cy² = x² + y

A: Given : cy2=x2+y   To Eliminate :  Arbitrary constant in given equation

Q: 3. Area between two curves. Sketch the region enclosed by x + y² = 56 and x + y = 0. Decide whether…

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Q: For the piecewise linear function, complete the following. if x ≤ 3 if x > 3 f(x) = Draw its graph.…

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Q: Solve the differential equation (d2y/dx2) - 7dy/dt = 0 if y(0) = 1, and dy(0)/dt = 1 A.…

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Q: In Exercises 9-16, verify each limit using the limit definition. For ex- ample, in Exercise 9, show…

A: To verify each limit using the limit definition.9 limx→4 3x=12 10 limx→5 3=3

Q: (1) Sketch the graph of f(x). Be sure to label the axes and that the graph is consistent with your…

A: We have to graph the given function.

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A: Given lines are L1: x=2-t ,  y=3+5t, z=4+3tL2: x=4t, y=1-20t, z=4-12t

Q: Evaluate: 1. lim [√x² + x − √x² + 4] = X→ +∞ 2. lim [(x²-In(x + 1)) cotx] -0-x

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Q: 10. dy dx xev (a) y(0) = -2 (b) y(1) = 2.5 (0)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: J + tan x)² sec x dx

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Q: Compute the first-order partial derivatives of the function. w = In (x7 — y4) (Use symbolic notation…

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Q: S x5 ex dx

A: We will use method of integration by parts. We will perform step by step process to finally solve…

Q: Solve the ff. Linear Equation: c. 2 2x³y = y(y² + 3x²)

A: We have to solve this given Bernouli's Differential Equation.

Q: The table shows the purchasing power of a dollar in recent years, with the year 2000 being the base…

A: We need to determine exponential equation.

Q: Example: A particle moves in a straight line according to the positon function s(t) 0.5 sin(6t) + 8…

A: We can solve this as follows:

Q: You can choose from two pairs of jeans (one blue,one black) and three T-shirts(one beige, one…

A: Given Data: Number of black Jeans=1 Number of blue Jeans=1 Number of T-shirts n=3

Q: Determine whether the set W is a subspace of R³ with the standard operations w = {(a, -a,0): a is a…

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Q: Use the Chain Rule to compute the partial derivative. ə -In (6u² + uv) = 0 du

A: To evaluate: ∂∂uln6u2+uv According to chain rule : If y = f(g(x)), then y’ = f'(g(x)).g'(x)

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: e the Chain Rule to compute the partial derivative. d -In (6u². + uv) = 0 du Orrect

A: Topic :- Application of derivatives

Q: Evaluate the integral. 82 (x - 1)(x² +81) dx

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Q: 26. 1 (₁7) + dy - 2xy) d + cos x - 2xy dx = = y(y + sin x), y(0) = 1

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Q: Let f(x) = x-4. You apply (in the order given) all of the following transformations to f(x) to get…

A: Given query is to apply the transformation and find the new function.

Q: If f(x) = (4x² + 5)5/2, compute the first and the second derivative of f(x). f'(x) = f"(x) =

A: Given query is to find first and second derivative.

Q: 5.8 or in the direction in which f(x, y) = 9x³y³ P(−1,1), and find the rate of change of fa act…

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Q: f(x)=2ln(6x) f′(x)= f′(2)=f

A: Given query is to find the derivative.

Q: Simulate the solution of the given problem using Excel such that when the given four data points (x…

A: we use exel to fit the equation

Q: -10 -5 6 3 0 Ny 5 X 10

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) 5.…

A: The given equation is; 6y2dx - x(2x3+y)dy=0.

Q: The amount of expenditures on national defense by a certain country (in billions of dollars) can be…

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Q: On equation (iv), why is d/dz of 3z^3 is equal to 3z^2, shouldn't it be 9z^2?

A: Yes, you are right. There is mistake in equation (iv). Correct solution is shown below.

Q: 4x² 1. Let y=f(x) = 4x+1

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Q: 1. Find the slope of the curve x²+ y² -6x - 4y - 21 = 0 at (0,7). Compute also the tangent line and…

A: Since you have posted multiple questions I can do first question as per our company guidelines.…

Q: K Let f(x) - f''(x) = 3 + 3 x6

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Q: Suppose that (g(x))² + 8x = x² g(x) + 4, 2 and that g(3) = 4. Find g' (3).

A: Given query is to find indicated derivative.

Q: 1. Find all roots: f(x)=x²-x+4

A: Dear student , as per bartleby policy we are allow to solve one doubt at a time. Kindly repost other…