1 2an112 니 a2 0.01 1 -0.01 X e x a.2 dx

Q: Use an appropriate trigonometric identity and substitution to evaluate the integral: tan’ r sec rdr

A: Given Indefinite integral as follows As we know that

Q: Use an appropriate trigonometric substitution to evaluate the integral: dx (1-x²)³/2

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Q: Given y = f(x), the [Select] at the point of (a, f(a)) is given by f(a+h) - f(a) h provided the…

A: The objective of the question is to identify the correct terms that fit into the given mathematical…

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: Please explain each step and graph the following: Graph the equation y= -4x2

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Q: Use substitution to evaluate the definite integral: [1+22dx

A: Given definite Integral as follows

Q: A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

A: Given,v(t) = -g.t -ve.lnWhere, g = 9.8m/s², m = 20,000kg, r = 160kg/sVe = 3,300m/sNow A.] the height…

Q: a) For the following functions, f(x)=√√2-x h(t) = t+1 2t² + t-6 2x + 1 x > 3 p(x)= x²₁-1<x<3 -3,…

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Q: Use the graph of f(x) above to estimate the value of f'(3) to one decimal place. f'(3) =

A: Given graph of f(x) to estimate the value of f'(3)

Q: . Evaluate the given definite integral. Show the CTS steps clearly where needed; show the…

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Q: Yaster Car Sharing offers a membership plan with a $54 per month fee that includes 13 hours of…

A: Here, car Sharing Yaster Car Sharing offers a membership plan with a per month fee that includes…

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: By using properties and algebraic methods to find the following limit., where

Q: 2. A spring has a natural length of 10 cm. It takes 1 J to stretch the spring from 10 cm to 15 cm.…

A: Given:Length of spring - 10cmWork done to stretch the spring to 15cm - 1J

Q: Consider the piecewise defined function g given by the formula g(x) = x² + ax+2b S -x² +5a if x>3 if…

A: The objective of this question is to find the values of a and b that make the piecewise function g…

Q: What is the tangent unit vector for u(t) if u(t) is equal to the following

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Q: Solve the initial-value problem for y as a function of x. y (x²+49) = 1, y(7) = 0 dy dx

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Q: Use integration by parts to evaluate the integral: [₂ đã xed

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Q: a) [x√x-1dx

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Q: Find a unit vector e, where v = ev (6, 7, 6)

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Q: 1 5 Given f(x) = x + 1, a = 0,b = 4; n = 3; 4x₁ = 1, 4x₂ = 1,4x3 = 2; x† = 1₁x₁ = 7,x² = 3, find the…

A: Consider the function

Q: 30. Find an equation of the plane that contains the points (-2, 1, 4) and (0, 3, 1) and contains a…

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Q: During each cycle, the velocity v (in meters per second) of a robotic welding device is given by v =…

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Q: Given f(x) = 4x²; a = - 3₁b = 4, n = 4; 4x₁ = 2, 4x₂ = 1, 4x3 = 3, 4x4 = = 1; x = = find the…

A: The given function  and the points  and the sample points .The objective is to find the value of…

Q: (sec² (sec²(t) i + t(t² + 1)³ j + t7 In(t) k) dt

A: Vector integration

Q: For y = f(x), we define the [Select] of f at x, denoted f'(x), by f(x+h)- f(x) h if the limit…

A: For function y=f(x), they have been defined f'(x) of f at x, and it is called derivative in…

Q: Find the angle between the vectors. (Round your answer to the nearest degree.) a = b = X O

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Q: Determine whether the equation is exact. If it is, then solve it. e'(9y-5t)dt + (2+9e¹) dy=0

A: Given differential Equation is as follows

Q: ||v|| = 4 ||w|| = 2 The angle between v and w is 0.2 radians. Given this information, calculate the…

A: Vector dot and cross product.

Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total…

A: Given that the revenue and total cost functions are (a) The profit function is

Q: A tank is designed with ends in the shape of an isosceles triangle with height 20 meters and width,…

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Q: The price of a product in a competitive market is $200. If the cost per unit of producing the…

A: Cost per unit of producing the product The price of a product in a competitive market is where x is…

Q: -5 -4 -3 -7 -2 -3 12 4 5 Use interval notation to indicate where the functin above has... A)…

A: The graph is said  to increase if the graph goes upwards as  we move from left to right along the…

Q: Evaluate the expression for 2=4 -7₁ and w= 7+3₁ Simplify completly Z+w =

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Q: The consumption of tungsten (in metric tons) in a country is given approximately by p(t) = 136t²…

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Q: f(x) = {0.42-3.8, [0.6 f(2) = lim f(x) = z 2- lim f(x) = 2 2+ lim f(x) = x 1

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Q: Let f(x) = √24-x. Compute f'(8) using the limit definition f'(8) = Find an equation of the tangent…

A: f(x)= ✓(24-x)We have to find f'(8)And equation of tangent line at x=8

Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: The previous exercise asked you to find a formula for R(x), where its derivative is 100e*+5 (1 +…

A: The given derivative function is .The aim is to find the principle antiderivative of .Formulas used:

Q: Let R be the region bounded by the following curves. Use the shell method to find the volume of the…

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Q: Use scratch paper to complete the table below, and estimate the value of the limx→o+ f(x) where ƒ(x)…

A: The objective of this question is to estimate the limit of the function f(x) = 5x * ln(x² + 4) as x…

Q: Use Laplace transforms to solve this equation 3f(t) + 2f(t) = t where f(0) = -2

A: The given differential equation is

Q: Find the arc length of the curve below on the given interval. 1 3/2 y = = = (x² +2) ³/² on [0,6] The…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: 3) lim X→-1- A) ∞ 5 x² - 1 B) -1 0 D

A: Limx-(-1)-1 [5/(x2-1)] [5/(x2-1)]

Q: Revenue The revenue (in dollars) from the sale of a infant car seats is given by R(x) = 67x -…

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Q: Find the constant of variation when one exists and write it in simplest form. 3xy = 21 Direct…

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Q: The sphere of radius 2 centered at (0,0,1) is pictured below. Select the equation which best…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: 8. Solve each of the following inequalities and write your solution in interval notation. a)…

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Q: Use the graph of f(x) above to estimate the value of f'(0) to one decimal place. f'(0)=

A: To estimate f'(0)